For your original question, there is a setting in the company profile called 'Include bank in Control account'. This option is so that when you create a manual check batch (or system check run) for a certain bank, only control account sets with that bank will be selected. Therefore, you can prevent some vendors from being paid by that bank.

Typically this would have to be done at year end because Adagio Payables prevents you from editing the Control Account sets when there are open batches or posting journals. Unless you want to clear everything to make these changes, the time when you have to do this is at year end.

For your check reversal q'n, when a check is reversed, there should be a new RC transaction created on the vendor record. The original payment should be left alone and the invoice should be unpaid. Both the RC and payment transactions will have a current amount of zero, meaning period end or year end will move them to history. Reversed checks will appear on the Check Reconciliation Posting Journal report.