Can the IRS take your unemployment checks if they have a levy on your bank account?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Once funds have been deposited in an account they can be taken. You can forestall that by informing your bank that only exempt funds are being deposited into the account. But if there are non exempt commingled funds then you have a problem.

You should not put them in there, it will be confusing and I doubt you want to have to go back to court to free the money up.