As for financial issues with divorce. Yes, get all the financial records you can and look to see if there is a suspicious pattern. (Frankly, he sounds too mentally incompetent to have done much that would be hard to find, but who knows - maybe he's got Fort Knox in that room!)
I would recommend getting as much of the settlement up front as you can. You have no idea whether he'll still be capable of working in the future, so a bird in the hand is better. If you would be due spousal support, try to get a lump sum buyout instead. Make sure there is life insurance on him to cover child support and other payments, and pay the premium yourself to make sure he doesn't let it lapse. If you can't afford to buy him out of the house, it is fairly common to draft an agreement where you and the boys stay in the house, split costs and then sell and split the equity when the boys graduate high school. This is not right for everyone but it's an option.
If he does end up paying you spousal support insist on an automatic draft from his paycheck.
If you can get him to agree to help pay for college, get it. My ex insisted on it (even though both lawyers were against the idea) and the irony is, it was likely HIM not me who would have flaked on the kids' college expenses without this agreement.