Retirement tax questions

No.  As previously answered, when considering how Roth conversions are taxed and the pro-rata rule, all your IRA balances are combined, no matter how many different accounts they are spread out over.   If you have deductible funds in bank A, and you contribute non-deductible funds to a different account with bank B, they are considered one account, and the conversion will use the pro-rata rule by combining A+B.