While serving notice period in TCS I have to go to the office also ?

Not needed. They can't put you behind bars if you do not go to office, least they can do is not to give experience letter.
I think comfort working from home is more important than experience letter ...right ?

No need man no one can do anything nothing will happen

Do what u can , nobody knows it's purely project mgmt thing . Usually as long u complete ur work during NP, u will be fine

Yes

Notice period you still get salary, so the rules are same too :)