Can a bank take money out of a private account to pay a business Credit Card dept?

yes, but it defends on how much moneythey gonna use.

If you owe money & refuse to pay, unless you fight it in court, they will have their lawyers file a lawsuit against you. If you have reason to fight back, there are ways to do it & win. However, if you owe it, don't fight it, try to work it out & many times they will work with you -- if you are honest with them.