HappyGramps is wrong again. Banks and credit unions are perfectly able to be IRA custodians.
I think what you are asking, though, is if you may electronically transfer money from your bank account to the Roth IRA custodian for your parents' IRAs. The answer to that is no. The accounts must be in their names.
You can, however, transfer money into their regular bank accounts as a gift. They could then choose to electronically send that money to their respective Roth accounts - presuming they are eligible for Roth contributions.
ROth IRA is funded with the employee's (w-2 wage earner) money, in their name, not a joint name, once established it accumulates tax free and withdrawals are tax free, the employee pays tax on the money which goes into the account. Now, if you have a parent who is a w2 wage earner, then yes, they could open an account in their name. check irs.gov.
IRA's have nothing to do with bank accounts ; IRA's are managed by brokerage firms..........you can contact some of them to get info for your folks
They have to set it up, in their own names.
That's very generous of you. But, it's got to be their accounts.
No, you cannot. The accounts must be individual and in their respective names only.