Hi Priti,
I opened it in Scotiabank. They have StartRight program for newcomers. I didn't notice any Indian bank except ICICI Bank. You can google it.
It's better you take travel insurance. I purchased it online from ICICI Lombard. It comes for 90 days. It's not required if you are going to Alberta and some other places. Health insurance is from Day 1, but in Ontario, there is a wait period of 90 days.
SIN card is not an identity card. You need the number to give to your employer. You can get it updated in your bank account. For opening bank account, you just need passport and COPR.