I think there is no bank today that accept bitcoin for an investment especially to local banks, but I think a month or maybe a year from now banks may accept bitcoin as a transactions.

In my country, no bank is accepting bitcoin yet.

Banks operate centrally, and Bitcoin is decentralized. My computer wallet is ‘bank’. I don’t even need to go to the bank to keep my bitcoin there. The Bitcoin wallet is so efficient, fast, safe and much better than the bank.

Maybe a country's bank has accepted bitcoin. But the bank of my country has not done this yet. I am not aware of it. But bitcoin price is increasing day by day. The time will come, all banks around the world will accept bitcoin. Bitcoin has many people work with it for a long time. They are waiting for bitcoin to get legal recognition. Bitcoin did not get legal permission in most countries except in a few countries. So if a country's government does not accept bitcoin, then the bank of that country does not have the power to accept bitcoin. Because all banks depend on the government of their country.

May be in such countries where bitcoin is accepted as legal currency, i think that there may be some banks who are accepting bitcoin. But i do not think that any country where bitcoin is not consider as legal currency, they may not be accepting bitcoin, in future may be these banks also start accepting bitcoin when the government of these countries will start legalize currency.

I don't know if there is a Bank that accepts bitcoins because I know there are banks that are against bitcoins because many people invest in bitcoin rather than investing in a Bank.

for now the bank can not cooperate with bitcoin because bitcoin has not been authorized in my country, but for other countries it is possible that it can be done

I was not been able to heard that bitcoin is already accepted in any banks but i am hoping that banks will accept bitcoin in the future, it will be more convenient to banks and any depositor if that may happen.

No idea,  i am not familiar with that and never heard any banks that officially accept bitcoin deposits or payments but maybe in the future it will happen, banks will surely accept btc.

Yes, some bank accept bitcoin. Just like here in the Philippines, some banks that I know which are accepting bitcoin is Security Bank and Banco De Oro.
Maybe they are the banks which realize the great value of bitcoin. Although accepting bitcoin is not totally implemented in other banks, I believe someday they will also accept bitcoin in their transactions.