Does Indian banks buy back the gold coins sold by them?

Hi, I am planning to buy some gold coin for investment purpose. To make sure of purity, I am planning to buy from Banks. As its investment purpose, I will be selling it after I gain handsomely / in emergency.
So does anybody know – which Indian Banks buy back the gold coins sold by them?

How do I sell gold coins?

I keep hearing that gold is a good investment. Banks sell gold coins. If I buy 1, where do I sell it later to get a profit? I want to buy & sell through safe secure channels like banks.

Where to buy and sell gold bars/ coins in Delhi?

I want to buy gold bars or gold coins in Delhi. Some say that banks are selling it for higher price, so I guess I should opt for jeweller shop. Any idea, which jelweller shop can I trust? Also, how do I know if the gold bar is pure?

Do I need a PAN card at the time of buying and selling gold bar from jeweley shop?

Do I need to pay tax if at the time of selling gold bar? What if I got cash from buyer?