Focus - So nice that you've found such a nice guy! Sounds like he has done all the right DB things since his breakup, even though he hasn't been here! Shows he has good character.
About the divorce - do the paperwork yourself and send it. If you don't want to contact him for the address, can you ask someone else to contact him for you? I know it feels unfair that you have to do the work, but it will free you.
Also, be careful. I would interpret his question about your mortgage balance as worrisome; could he be trying to make a claim on it and wants to know how much equity is in it?
Sounds like you should be safe if joint funds were never used to pay the mortgage, but be careful.
Also - congratulations on your almost paid off house! Check out the Mr Money Mustache website, I think it might resonate with you !
