I certainly understand bad luck - we have been through some really tough times as well, medically, too. Three years after our really bad luck happened, I feel we're finally in a much better place (not just financially). Having been through some pretty complicated medical things too, I would do these things. Are either of your hospital stays covered at all by insurance? Has insurance already paid their portion? It takes months, sometimes up to a year or more for all the "final" bills to come in, so that may be part of the reason your fiance doesn't know the exact amount. It's absolutely worth appealing the insurance companies to pay as much as possible. They count on people not appealing, so if you appeal, you might get it. We get denied for almost everything and have to appeal everything, so I can tell you, it's worth it. Also, is there not a maximum out of pocket? If he or you were laid off, then that insurance you should still be able to access via Cobra or whatever, right? It's also worth going through all the explanation of benefits one by one, and determining the exact amount you are liable for and disputing the difference. I cannot tell you how many "mistakes" I have found here.
As for collections notices, they will call ANYONE they can find with ANY relationship at all. That doesn't mean they can actually collect from you. Call them and tell them that. You don't have to mention you are engaged. I don't believe they can come after you (unless you are guarantor on something) and tell them that, otherwise THEY need to prove what you owe and why. Then tell them to stop bothering you.
I have no other advice about the other stuff, but if you have time and effort, you might be able to save some of what you owe medically by doing those things.