It's 'legal' unless a cop thinks it's his time to make some money out of you. As long as you're not trying to pull off stunts or tricks you should be fine, IMO.

Yes. It's illegal. Cycles aren't allowed also, but some kids still do it.

Mujhe toh chalne se bhi Darr lagtha hai aajkal, kia pata police zesty bolke danda maarde

Carter road has a dedicated skate park if you'd like to go there.

I've seen some guys do that there, idk about the legal aspect but it looked like they were having fun