Why does all the sensor registers from MPU6050 returns 0 to me? and why I can't write to the registers?
It seems that you are saying that your hardware is OK (but you haven't supplied a schematic and a photo of your prototype) and saying that your software is OK (but you haven't supplied any code). They can't both be OK, if you are having a problem! However you have not supplied enough information for sensible analysis. :-(

I suggest you start to solve your problem this way:


Stop using your own software.
Find a "known working" software example for accessing the MPU6050 using Google - lots of people have published tutorials etc.
Use that software example (unchanged) on your hardware.
If that software works, then the problem was your original software.
If that software does not work, then your hardware has a problem (your software might also have a problem, but you cannot know at this stage).


Using that "flowchart", you will discover where to start looking for your problem.

If you have an oscilloscope or logic analyser, then you can view the I/O on the I2C bus, to confirm what is actually happening. It seems possible that you have a problem with your I2C writing, since the data in registers seems unchanged after you think you have written to them.