A. There is no “Bitcoin bank”. It sounds like you need to get to grips with cryptocurrency first before buying any.
B. Cryptocurrency doesn’t use IBANs because it’s not fiat currency.
C. I’d recommend not doing anything as you don’t have the basic knowledge yet to know how to use a cryptocurrency wallet and send and receive funds. If you mess it up, you will lose all your funds.
D. Your bank will not know anything about cryptocurrency and will probably tell you it’s a risky investment. They won’t be able to help you.
E. Banks don’t keep your money in a vault. That’s not how banks work. They probably haven’t done that in decades. All your fiat currency is stored digitally. Not to mention the fact that banks use fractional reserve banking, which means they lend your money to other people.
In short, if you already have NEX or some other tokens, just keep them in your NEX extension. If you don’t know how to use other wallets, you will end up losing your funds or making mistakes. NEX is already non-custodial, so it’s fine.