If he hasn't been tested recently, there's no way of knowing what he does or doesn't have. Many STDs can be asymptotic for a long period of time. You could always insist that he gets tested for all the diseases he can be tested for. If he has none of those, then the chances of him having other ones are probably much smaller. If he comes out having something and you know you don't want to put yourself at risk, that will answer your question.
You haven't said why you think he might be mentally unstable, but that seems like a bigger red flag to me than a person's past. That would be enough reason for me to hold off on having sex with someone for a while anyway. Figure out what type of a person you're dealing with before you get too involved.
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy