Wheter you allowed BoA access to all your accounts depends on the documents you signed when you opened the account. You've clearly authorized them to access your checking account for purposes of paying your mortgage because you have autopay. As for whether you've linked any other accounts, you're going to have to review what you've signed and agreed to.
If you have any doubt about it, then move your money. There are plenty pf banks out there.
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Yes, if you are in serious default on a loan from a bank and have money saved at that same bank -- the bank generally can access and transfer funds from a savings or checking account. This process is known as "Setting Off." Therefore, to be safe you should close all BOA accounts and move your funds to a separate financial institution. Then I would recommend that you contact your bank to see if they will work with you to make repayment arrangements.
Generally yes, under set-off or a cross-collateralization clause in regard to the loan they can take money from one of your other accounts if you are in default on another loan/account. It does depend on the situation, but generally, yes. You should consider forming an entity for your business/business accounts, such as a Limited Liability Company. This would be an entity separate from your personal assets. Even then, you will need to look out for personal guaranty clauses and such.