I think you have answered your own question. For the roof at end of functional life, that is sort of a catch all for the inspector to say you cant hold him responsible. From your inspection could you get another year or two out of it and maybe patch here and there as needed until you get the property cash flowing or would it need done immediately? I bring that up first because that is not really an issue.
However, with the health department, fire department, building department, and all the other departments coming down on you the day you take ownership, that is not a good thing. If the numbers are strong enough then it may be worth the hassle, but if you are using cash to purchase something you will have to dump the remaining cash in it may be time to cut the ties.
You should buy the worst house in the best neighborhood but it sounds like you are buying the money pit in the worst area.
No paperwork being supplied is a problem, there are obviously more problems then he is letting on. He was hoping you would not be diligent and find out these things obviously but now he either needs to pay or renegotiate. It would not be the first time someone came back after a contract was made and ask for adjustments. One or two small things can come up, but you started by saying you have a triplex under contract and ended with a duplex with major issues.
Don't be labeled the slum lord by the inspectors, they are the ones you have to play nice with. If you get a bad name and on their list they will haunt you forever. They are only doing their job so I do not fault them, but unless your kids play t-ball together 2X a week you should not be on a first name basis with them and it sounds like this owner is.
$800 net with $90K contract plus repairs don't sound like a solid deal to me. There is not much room for error and if you end up with even one vacancy it sounds like you won't be making anything when its said and done.
If it was me I would pass or renegotiate. With new ownership see if the inspectors would give you some time to conform and look at increasing your income throughout the units in addition to signing new leases with the tenants to make sure you don't end up vacant at ownership. I prefer to get my own tenants in the property however if you must take it preoccupied make sure you protect yourself as much as possible.