Is the flow of time regular? Is the flow of time regular? How would we come to know if the our galaxy along with everything in it stops for a while(may be a century) w.r.t to the galaxies far beyond our reach. Is there a way to know if flow of time is smooth,or irregular?
PS I would describe myself as an illiterate physics enthusiast, so I hope you'll forgive me if my ignorance is borderline offensive.
 A: 
Note:  This answer addresses the question in its original form:

Is the flow of time regular? How would we come to know if the whole
  universe along with everything in it stops for a while(may be a
  century). Is there a way to know if flow of time is smooth,or
  irregular?


Flow with respect to what?  Regular with respect to what?

How would we come to know if the whole universe along with everything
  in it stops for a while(may be a century)

A century as measured by what?  If the "whole universe stops", what would "a while" mean?  "a while" according to what?  What would "stops for a century" mean?
If you think carefully about the premises of your question, you'll find that you're imagining a 'meta clock' that doesn't stop when you stipulate that everything 'stops' (stops according to what?) and by which one can judge the 'flow' of ordinary time.  Closely examine that premise.
A: The simple answer is that in our everyday world where velocities are much smaller than the velocity of light, yes time is as regular as space. If you rule a football field as 100meters by 100 it will stay that way whenever you measure it ( unless there is an earthquake of some such disruption). We have rulers defined in France for the meter, and we have clocks defining the time. Starting with pendulum clocks whose frequency does not change and it measures time to the Cesium clocks that measure time even more accurately, the flow of time is constant.
If one goes to special relativity and has two systems moving with relative velocity close to the velocity of light  time slows down when each system looks at the other  from a framework at rest, and space is seen as distorted in the direction of motion of the moving frame,  but that is another story. Within each framework time flows uniformly.
In General Relativity where there is gravity it means that space and time are distorted so as to generate the gravitational fields we see, and that is still another story.
A: Have a look at my answer to Is there a proof of existence of time?.
The problem with your question is that the concept of the flow of time is an elusive one. We measure flows with respect to time, for example velocity is $dx/dt$. So how can we measure the flow of time? If we simply say it's $dt/dt$ then obviously that is always one.
The only possible answer to your question is that no, we cannot know whether the flow of time is smooth or irregular. But this is a somewhat misleading answer since the flow of time isn't well defined.
A: Absolutely no. The best known counter-examples are the clocks on board the GPS satellites. If the flow of time was "regular" , they'd run just as fast as any other clock. In reality, they run slower - precisely as predicted by relativity theory. So there's a clear discrepancy between us down here and a satellite that's just a few hundred kilometers up.
A: Under Special Relativity the flow of time should be inferred to be regular for a single observer because the speed of light is invariant with regards to the single observer.  Observers in the same reference frame will measure the same value for the speed of light, and as a consequence experience the same flow of time.
Your perception of time may vary as noted in the (perhaps apochryphal) Einstein quote referenced elsewhere, but at a physical level, your physical experience of time is regular.
A: As BICEP2 has shown, spacetime has been significantly irregular, enough to change how electromagnetism propagates.  Especially considering relativity, time is not regular.  Deviations from a "uniform rate of time" are not easily observed, but different rates are now measured daily worldwide: GPS must account for a small (per second) rate difference between satellites and Earth's surface, which would introduce large (per kilometer) errors in location.
A: 
Is the flow of time regular?

Picture a leaf floating downstream on a river in the pitch dark. As the river gets narrow it speeds up, and as it gets wider it slows down. The leaf has no light to see the shoreline so from it's perspective there is no change in the flow of the river.
Now what if the light turned on?
The leaf could now see the shoreline, but from a physics point of view. This shoreline is the background radiation of the universe. It's so far away that as we move down the river we can't perceive any movement in the shoreline. Therefore, we can't tell if the river speeds up or down.
The only way would could tell is to look at the shape of the shoreline. Are there points on the shoreline moving closer and/or further apart. How could we tell the difference between changes in time or changes in the shape of the shoreline?
That is why people study the big bang. To predict what the shape of the shoreline should be, and then see if there are any unexplained changes.

How would we come to know if the whole universe along with everything in it stops for a while(may be a century)

Time for a human is perceived not in the current moment, but in the memory of previous moments. Humans remember time passing as our brains record past events. If time stopped for one individual, then it would be like pressing pause on a VHS recorder, but when time stops for the universe then everything stops. Even the VHS recorder would not record a gap in the video since the inputs to the VHS paused as well.
The universe could stop and continue. We'd have no perception of the events. Since it's a completely untested event. It means it never happened. Even if it did.
A: Our perception of time is irregular. "A watched pot never boils" and the effect of being able to perceive minute details when in a crisis - pebbles shot from a wheel and the colour of a band around the tyre as you are about to be run over for example.
A: Energy, Space and Time all are granular. The difference betwenn them are the unbelievably small dimensions of the smallest space and time steps, as opposed to the rather largish smallest energy quantum h. Which is large enough to have been proven experimentally 100 years ago. (Which is what earned Einstein his Nobel prize.) 
The granularity of time and space will will be out of reach for experimental physics for pretty much all times.
So, there is no flow of time, the universe ticks. But if these ticks are and have always been the same ist not known.
