Streamline all the money talk. No, you do not get to ask him to contribute to a TV anymore than he gets to ask you to contribute to his dinner out with OW.
No, you do not get to tell him how to manage payments/accounts. Do it yourself or let him do it. But, get his business out of your business ASAP.
The money stuff is A MESS. Clean it up immediately. You have your budget, he has his budget. You pay your bills, he pays your bills. You have different bank accounts.
This financial stuff is a HUGE priority. Neither of you needs the added emotion and dissent of having mixed finances. He is giving you support of X dollars a month. The only money talk should be whether or not he has made that transfer. Change names on accounts as needed to make it so, this week.
If he had taken care of the credit card thing, he would have told you. Either take care of it yourself OR if it is none of your business, ignore it. If it is a matter of transferring debt to his name that he agreed to on the separation agreement, notify him in a businesslike way that it is time for him to satisfy that obligation. If he does not, have a L send a letter.
Re the computer, just tell him you need it back, do not bargain with him on it.
