Time travel, Just a sci-fi dream? A possibility?

Have you ever heard of the Grandfather Paradox?

Maybe yes, or maybe no.

For those who don't, I would like to make a restatement of Grandfather Paradox, and for those who do, I would like to ask questions on it, out of my curiosity.

Here's the famous Grandfather Paradox:

"Imagine, if I could go backward in time, I want to experiment with a paradox. Let say, I remember my grandpa first met my grandma on XXth day XX Month in XXXX year. Now, I've just invented a time machine and want to go backward in time, to one hour before my grandpa and grandma first met each other. When I met my grandpa, I say to him, 'why not we go for a race instead?' And he agrees, so the first meeting with grandma was avoided. 

Now, here's a big problem. If my grandpa didn't meet my grandma, so why do my father exist, if at all? And if I'm not here, how would I invent time machine and go back in time, and prevent my grandpa to meet my grandma?"

Well, surely this paradox poses headache to all sci-fi fans, physicists, mathematicians, and all humans who wish to change their past. So here comes the questions, explanations I've gained from numerous resources:

1.) Time travel to the past is forbidden in physical reality. In Stephen Hawking's chronology protection conjecture, he challenges mathematicians and scientists to disprove time travel to past. But so far no one can disprove the arrow of time, and even Einstein has proved that time is more dynamic than it is. So, if mathematics support strongly a theory (or never seem to be able to disprove it), why is our daily life experience seem to defy time travel, based on our intuition? 

2.) Another physical law seems to defy time travel. For those who know Entropy concept, you can skip this first few sentences. But as for general readers, I will make a lucid elaboration here, using daily life situation. Imagine you scramble your egg, and cook in in your frying pan. So, based on your daily life experience, can you reverse the process of cooking the egg, unscramble the egg, and put all the egg shells together? A big no, unfortunately. So, after giving this prominent instance, I will give a more general statement. According to second law of thermodynamics, the entropy (the measure of disorder) of universe will tend to increase (i.e., things tend to disorder), and never decrease. Even if you spend energy to make things back to order, the energy spent will be converted to heat energy, and increase the disorder of surrounding. So, if that is the case, time travel seem to work only in one direction, but in contrary to our daily life experience, the arrow in this law can be pointing towards either past, future, but not both. The question for this second is, if entropy works in one direction, why can't the law proves (by providing concrete mathematics) that it only points to future, and not to the pass?

3.) After providing counterexample of time travel, I will provide an instance that vindicate time travel. Recently, one of the most bizarre theory, string theory, has evolved into a super theory, the M-theory. In M-Theory, there's a possibility of creating something called wormhole, by breaking the Planck Energy Barrier (though current technology, even the particle accelerator at CERN, Geneva, could not break this barrier). If our technology could advance to a level, so advanced that The breakdown of Planck Energy Barrier has become a commonplace, so why can't we open up a wormhole? Well, the entering wormhole itself kills you, tearing you apart, and you'll probably get distorted. So, if one day wormhole is made possible and accessible, then the paradox will arise. Let say this time you try to kill your grandpa instead, a few weird possibility rises. One is that you will feel a mysterious force to prevent you to do so (though this statement has no justification, purely based on my imagination). Another is that the moment you do time travel, the past you know will part away into a parallel world where in the parallel world in that parallel universe, you don't exist. So in any of these 2 (or maybe more) outcomes, here comes my question, if let say the past parted and parallel world do exist, why can't we see them?

4.) Here's a final question, I will keep this short and simple, if people from future can travel through time, why can't we see them? (Or maybe they are forbidden by future law to reveal their identity, but rules are made to be broken, so some of them must've reveal their identity if time travel is possible.)

For those who made your way here by reading through this post, I would like to thank you for your time and effort. But most importantly, I need feedback, comment, speculations, criticisms and constructive comments on this Paradox and Time travel. Is there anyone out there to demystify my curiosity, then?

A simple explanation through equation on time dilation. 2 persons having contradicting views  on how 'fast' time has passed. Einstein Special Relativity for Time Dilation