You are misinterpreting a fundamental concept in special relativity. Time is relative to different observers. Nevertheless, no matter how fast you go (as close to the speed of light as you wish), your perception of time is unaltered. You will see your clock arms tic-tac precisely the same way.

There is absolutely no reason to state that all events in the Universe would be simultaneous. Even for a ligh-beam. Draw two orthogonal axis for an observer at rest, vertical being the time axis and the horizontal for one spatial degree of freedom. Draw a light-cone (or one-quarter of it). Make several points in this sheet representing different events. Now, over it, draw a new pair of axis for a moving observer. The higher its velocity with respect to the first, the more tilted should its axis be towards the light-cone (since the speed of light should be the same for all observers). Now project the events to this new axis of time. Definitely this observer will have a different perspective of what events are simoultaneous compared to the first one. But clearly all the events in the sheet don't fall into the same time coordinate point.

You can find these diagrams in any basic relativity book.

That means, the singularity doesn't exisit according to laws of physics???

I understand what you are taking about. I agree that if I am travelling at the speed of light, my watch will still tic-tac precisely the same way when I was at rest with respect to the earth. But How will I observe a person's watch ticking on earth when I am at light speed with respect to earth. My 1 second will be how many seconds for the observer on earth????

If you are not at the speed of light, but as close as you want to the speed of light, just apply the lorentz transformation. As you are at rest in your reference frame, it would be as if the other observer were moving really fast so that its time would be dilated (and by no means you will see every event in the Universe located at a single timespot).

The thing is, you cannot apply SR to an observer moving at the speed of light. Why? Firstly, because nothing massive should achieve such a speed. Then you say "Ok, but it's just a thought experiement". Nevertheless, you can work out your math and see that anything (even massless) moving at the speed of light has infinite acceleration, being clearly not an inertial observer.

Singularities should not exist in the physical world, that's where you limit the applications of your theory.

***As you are at rest in your reference frame, it would be as if the other observer were moving really fast so that its time would be dilated***

I told I am at light speed (i accelerated to c) and the observer is at rest on earth. So I should see his watch running faster than mine. (At light speed means his watch should run at infinite speed)

I may be naive but if you are traveling at light speed you cannot observe the tic-toc of a clock on earth because although you might be able send a signal to interrogate the clock on earth, the clock can send no return signal to catch up with you. Once you attain light speed the on clock earth will neither tick nor tock and ∆t → 0.