A: I'm not a fan of either term as I find they just confuse things. Durable usually is referring that it remains effective after incapacity. Sometimes general is looked at as terminating at becoming incapacitated. Another term which comes up is springing which this one makes more sense where it isn't effective immediately but upon a date or occurrence (usually someone being deemed incapacitated). I don't think I'd ever create a POA where it terminates at incapacity since that's when I'd need it to work. Now you say your mother has dementia. Will she understand what she is signing and the purpose of the document? If not, she doesn't have the required mental capacity to establish a POA and will have to have a guardian appointed by the court.
A: Did you purchase the property before or after the fire? If before, did you have insurance? If after, what was the agreement you had with respect to the insurance proceeds the Seller was to receive? The Warranty Deed is what is offered when there is a transfer of real estate and the seller warrants ownership to another. Frequently this will also involve title insurance to back up the warranty deed if there were other claims against the property
A: Yes, you could create a promissory note and terms in that note for repayment of back rent. That would create an obligation for her that if she defaults, you'd file as a breach of contract rather than an eviction at that point.
A: If your lease doesn't allow a sublease, you can't do it. I'd just approach the landlord and see what could be done. If the person moving in would be willing to sign a one-year lease and do the typical background check, the landlord may let you out of your lease.