Are quantum fluctuations completely uncaused events? I read here that particles/antiparticles appear and annihilate each other spontaneously in empty space.
Since particles appear and disappear in empty space, it would seem that empty space has some  form of energy. Otherwise these particles' fluctuations appear to be completely uncaused events, which defies reason.
Does space have some form of energy, or is this phenomenon completely uncaused?
 A: What is really being said is that it is not an uncaused event in the vacuum, but in simplistic terms, it could be said to be more a property of the vacuum. No event is taking place as such. Describing it as an event is trying to put it in simplistic terms, which while it may help in understanding to some degree, is not an exact description. You could equally well (and again not with accuracy, but as another way of trying to describe it in a word) call it the texture of a vacuum rather than an 'event' – looking at it like that means you don't need a cause.
A: It's not quite right to say that "particles/antiparticles appear and annihilate spontaneously" for the following reason:
Particles and antiparticles are modelled as excitations of quantum fields.  The things that are being described as appearing and annihilating in the vacuum are disturbances to these quantum fields, which are sometimes called "virtual particles".  Virtual particles are not particles.  A particle (or antiparticle) is a special type of excitation or "wiggle" which has a life of its own - it can travel off quite happily.  (Think of wiggling a slinky toy and watching the wiggle travel off).  The virtual particle is more of a twitch that didn't quite make it to being a fully fledged wiggle.
Now no analogy is perfect, and this one certainly isn't either.  
1  A quantum field might have an excitation which is more analogous to a wave all along the slinky, rather than a small wiggle travelling off.  This is also a like a particle/antiparticle.
2  You might get the impression that the field is changing with time and these virtual particles are twitches that you could "see happening".  However it's more subtle than that - actually these quantum fields are subject to the uncertainty principle, and the "twitch" that is a quantum vacuum fluctuation is merely a potential field configuration arising from the uncertainty principle.

these particles appear to be a completely uncaused event which defies
  reason

The vacuum fluctuations do not have any cause (other than that their existence is mandated by the laws of physics).  However, it's not correct to say that they're "events", for the reason I mentioned - they're uncertainties rather than things happening as a function of time.
To address your point about energy, you are right, if you apply general relativity these vacuum fluctuations contribute an energy which will gravitate.  This causes a discrepancy which has been called the vacuum catastrophe
