Does the Indian "UR" for town has its roots in the Biblical town of the same name?

Answer 1

Probably not.
Hebrew had a little influence on several languages including English, German Arabic etc, but those languages drew that influence from the bible or from the European Jewish communities.

I can't imagine a reason for the Hindu language to draw its word for town from a Hebrew ancient city.

I know several funny coincidences, but all of them are, well, coincidences. For example- the Aboriginal word for road is "Duruk", or something like that, while the Hebrew word for road is "Derekh". There is no known conection between the two (similar!) words.