Is heat death reversible by thermal or quantum fluctuations given an infinite time? I'm new here, so apologies if the question doesn't sound meaningful considering what physics is supposed to answer. I don't have a physics or mathematics background, but I did learn a few things about entropy and the different possible fates of an expanding universe from other forums. 
Now, assuming the heat death "fate" is where the universe is heading towards, asymptotically reaching towards a thermal equilibrium, will it stay in a state of equilibrium forever? or the will the "arrow of time" cease pointing sharply towards the future since decrease in entropy becomes likelier when a state of near maximal entropy is achieved (I'm guessing here) ?
The wiki article on this states the number of years that would take for a random quantum fluctuation to perhaps recreate another "big bang" and restart the universe as $10^{10^{10^{56 }}}$ . I realise that's a RIDICULOUS amount of time to even comprehend, nevertheless it is still a physical possibility and $10^{10^{10^{56}} }$ years are only a tiny fraction of time when compared to an infinite amount of time.
Finally what I want to ask: Is reality a one time phase transition from a vague potential with maximal degrees of freedom (big bang) to a crisp actuality with maximal constraint (heat death) with asymmetric, unidirectional time or is it infinite cyclic with symmetric time that reverses itself (by means of highly improbable, but physically not impossible mechanisms) after a finite period of time? 
I suspect this may be a borderline philosophy question, but figured might as well give it a try here before posting in more relevant forums. Thanks.
 A: The answer to this is "we don't know."
The cases you are describing are the extreme endpoints of the models we are using.  They come together slightly-not-aligned.  The real truth is that science will keep stabbing at these models, trying to make them align better by discovering effects that we don't know.
If I had to make a guess as to which of our models is "right," and had to put a wager on it, I'd put everything I own on "none of the above."  When you start talking about modeling the cosmos on that scale, it's almost 100% assured that theories will have to change to fit new evidence.  That's what makes science exciting!
That all being said, it may be worth noting that the "laws of thermodynamics" are actually the laws of equilibrium thermodynamics.  They govern what happens when a system at equilibrium is moved to another equilibrium.  If everything is in a continuous quantum flux that could cause big bangs at any moment (however so likely), we'd be a fool to say that we're in equilibrium!   There is actually a field called non-equilibrium thermodynamics.  Unlike its equilibrium cousin, non-equilibirum thermodynamics does not assume that things can be set up as homogenous structures which are at equilibrium within themselves.  They generally arrive towards generally similar answers (after all, this is science, and experimental testing will weed out one of any pair of theories which predict different results).  However, they do start to differ as you explore the extremes.  Determining experimentally which one is right may be impossible, because it may take all the time left in the universe just to do the test!
They do agree that any system whose state approximates one that can be described as having local equilibriums, will demonstrate equilibrium thermodynamics on local scales.  This can often explain a large range of non-equilibrium scenarios.  For instance, the stability of gunpowder inside a piece of ammunition is very well described by considering the gunpowder to be at a local equilibrium.  Apply an amount of energy and it will discharge the bullet, per the laws of entropy that you expect from equilibrium thermodynamics.  However, apply a small amount of energy and the gunpowder can behave in ways you did not expect.  For example, did you know gunpowder burns? It doesn't explode when you light it.  You have to contain the burn in a small volume (like we do in a gun) before the reaction shifts to an explosion.  Nonequilibirum thermodynamcis does a good job of predicting both behaviors.
So the question that matters for your question is whether the universe contains any regions which are not well-modeled locally as being in equilibrium.  If all regions are well modeled as such, then equilibrium thermodynamcis will model the universe well, and we will see heat death.  If, however, you cannot make this claim, then the answer is more complicated, and maybe those quantum fluctuations, never quite in equilibrium, can set something off.
Personally, I don't intend to wait for the answer.  $10^{10^{10^{56}}}$ years is a really long time.  Waiting for that would be like watching paint dry...
... well, not quite.  It'd be a whole lot worse than that!
A: The short answer: yes.
The longer answer: the problem with questions like these is not that they are philosophical (they're not). Given a particular theory of the universe, your question has a well-defined answer. The issue is that no single theory can be taken to be applicable to these time lengths. For example: it is well-known that if we consider a mechanical universe (i.e. classical a la Newton) which is moreover finite in extent, that it is not only likely that fluctuations will eventually decrease entropy, it is a certainty. This is called Poincare recurrence: the universe is cyclic. Of course, even if one would live in such a universe, the amount of years you'd have to wait to see such a recurrence is absolutely ridiculous. Nevertheless, given an infinite amount of time, it will happen. But there is a deeper issue: classical mechanics will never be an appropriate description over arbitrarily long time scales. Similarly for a quantum description of our universe: in a way it is indeed `obvious' that given the presence of fluctuations, whatever happened once can happen again. The problem is not just that it is very impractical, but rather that in order to believe such a prediction, you have to trust the theory to an accuracy that is completely unwarranted.
Of course there are also people who have wondered whether there is a reason to believe in a cyclic universe without resorting to fluctuations. E.g. in the past few months loop quantum gravity has gotten into the picture discussing exactly that (a version of the big bounce).
Nevertheless, some try to make it work based purely on fluctuation arguments. In particular there is Roger Penrose's work ("Cycles of Time"). If I remember correctly, there he tries to get away with 'having to wait an infinite amount of time for the proper fluctuation' by arguing that after the heat death, the universe is conformally invariant, in which case there is no scale of time (i.e. there is NO sensible distinction between one second and one hour) hence infinite time can pass in finite time and so voila a new universe springs into existence. And in case you hadn't noticed yet, Penrose is pretty awesome, so if you're into this kind of stuff, he's definitely a recommended read.
In fact, another good read (to get a general grasp on entropic reasoning on cosmological scales) is Roger Penrose's Road to Reality. There he for example very clearly discusses (the conventional viewpoint) that the big bang was not a period of large entropy (as you seem to suggest) but rather of incredibly low entropy. Moreover he underlines that this is one of the greatest unsolved problems. (The problem being: how did the universe get into this state? Of course fluctuations lead to one possible answer, and you might have heard of Boltzmann's brain in that context.)
A: Questions like yours allow complete non experts like me to waffle on,  but I will try to keep it short and coherent.
I believe its vital to remember that we can only see a small part of the universe, and we still have lots to learn, so the Plato's Cave story  comes to mind.

The wiki article on this states the number of years that would take for a random quantum fluctuation to perhaps recreate another "big bang" and restart the universe as $10^{5600} $.

I have no idea what started the big bang, but if was through the process of a "quantum flucuation", that figure above, to me (obviously this is a personal opinion, as no evidence exists regarding the initial event), would cast doubt on a quantum flucuation causing the universe we live it NOW.
So some other physical process might be involved that we may only learn more about when/if we gain increased knowledge about 3 problems we have yet to solve: dark matter, dark energy and the cosmological constant problem.

Now, assuming the heat death "fate" is where the universe is heading towards, asymptotically reaching towards a thermal equilibrium, will it stay in a state of equilibrium forever? or the will the "arrow of time" cease pointing sharply towards the future since decrease in entropy becomes likelier when a state of near maximal entropy is achieved (I'm guessing here) ?

I am not sure what you mean by  the arrow of time pointing sharply. Personally, I think, from my very limited knowledge, that the heat death idea was formulated a long time ago, and what effect recent discoveries regarding dark energy and accelerated expansion have on that idea, I don't know.  I pretty sure the concensus is that a heat death ending is likely, based on thermodynamic laws, but we still have a lot to learn re the problems I outlined  above and that might allow us more educated guesses in the future. 

Finally what I want to ask: Is reality a one time phase transition from a vague potential with maximal degrees of freedom (big bang) to a crisp actuality with maximal constraint (heat death) with asymmetric, unidirectional time or is it infinite cyclic with symmetric time that reverses itself (by means of highly improbable, but physically not impossible mechanisms) after a finite period of time?

I have absolutely no idea, all I can do is recommend you read up on  theories such as Penroses "Cycles of Time", whatever Hawkings latest theory is on the beginning/end of time subject, Ekpyrotic Universe  by  Paul Steinhardt and Neil Turok or finally (but certainly not exhaustively) Julian Barbours "The End of Time", in which he says time doesn't exist in the first place (that would sort out a lot of problems).
If physics is ultimately evidence based, which of course it is, then it must be, as we are severely lacking in evidence in lots of areas that your question poses, that  this a philosophical question.
A: The final state of the universe comprises cosmological hypothesis, since it is non-observable. The main determinant of this fare (going from the wikipedia article Ultimate fate of the universe) is the expansion factor, or the average distance between galaxies as time goes to infinity. 
$D_{\infty} = \lim_{t\to\infty} \overline{D}$
From a classical standpoint, let's suppose we allow entropy to decrease and mass-energy conserves approximately. If the amount of mass-energy within the cosmological horizon from any given point of view diminishes as $t \to \infty$, that is, if $D_{\infty} > 1$, then even if all matter within such a horizon were to collapse, one could not replicate exactly the observed Big Bang: there is missing mass-energy.
The classical Poincaré recurrence conditions are as follows:

1 A finite upper bound can be set on the total potentially accessible phase space volume. For a mechanical system, this bound can be provided by requiring that the system is contained in a bounded physical region of space (so that it cannot, for example, eject particles that never return) — combined with the conservation of energy, this locks the system into a finite region in phase space.
2 The phase volume of a finite element under dynamics is conserved. (for a mechanical system, this is ensured by Liouville's theorem)

Those clearly cannot be satisfied if the average distance between particles goes to $0$, or if the number of particles in the system decreases.
I don't have enough knowledge to answer on quantum fluctuations.

Is reality a one time phase transition from a vague potential with maximal degrees of freedom (big bang) to a crisp actuality with maximal constraint (heat death) with asymmetric, unidirectional time or is it infinite cyclic with symmetric time that reverses itself (by means of highly improbable, but physically not impossible mechanisms) after a finite period of time?

Therefore the infinite-cycle hypothesis rests on the expansion factor. I believe currently measurements indicate an accelerated expansion, which would mean no, the universe cannot be cyclic (given the stated assumptions).
