Bitcoin is hardly to be saved in a bank accept it is exchanged in a local currency of the land. This means that you must exchange bitcoin to the value of the local currency before you can make a deposit in the bank. i think bitcoin is mainly installed in the bitcoin wallet.
if the point is about saving bitcoins in some safed place - why not to chose one of bitcoin wallets? There are different kinds today. And it's right that novadays to hold bitcoins in a bank you need to cash it out in fiat of your country first, becouse there are no banks that would work with bitcoin directly today.
that is correct. There are various types of wallet and you can easily pick one for yourself. I suggest you should use the Electrum if you like pc wallet and mycelium for the smartphone. They are both great with a good security. Moreover, they allow you to keep the private key. You can also create a backup file to store your wallet in a safer place