Neighbor with Alzheimer’s– finances questions

Hi all, I'm the power of attorney for my neighbor (80) who has Alzheimer's. Here's the situation: she owns a townhome (worth between $700-900,000) outright. She has an annuity with about $200,000 in it. She gets about $2,000 a month from Social Security. No savings, no 401ks, no IRAs. She is inheriting about $30,000 that is now in a high yield savings account with a brokerage. She has $10,000+ in credit card debt. She owes about $7,000 in past due property taxes. Her monthly costs are at about $7500 due to memory care (I just moved her there). No family, no dependents. Her house was no longer safe for her to live in (various reasons, just trust me on this). I don't think she has the funds to spruce up the house so it could be rented out, and even if she did, it wouldn't generate enough monthly income to cover her costs at the memory care place. So here are my questions:

1. Any advice on selling the house to minimize capital gains taxes? She bought it about 40 years ago.

2. Do I pay the past due property taxes now, or just pay at close of escrow? I need to make sure she has enough money to pay for at least 2-3 months of rent at memory care place, plus enough to pay for eradicating the pests in her home before we sell it, but if I make enough money for her selling other items in her possession, I might be able to also pay off the property taxes. I'm hopeful she'll be able to get the late fees removed due to the diagnosis.

3. Do I deal with the credit cards that are going into default? Or do I ignore them? Her credit score is not good, but I don't know if that matters at this point.

4. I don't know the first thing about annuities. Any advice about that is appreciated. I don't think she'd qualify for their special thing they do when someone is in a hospital or in hospice, because she's not dying or receiving treatment. Do I pull the money out and eat the huge fees, so she has more accessible money if we start running out before the house sells?

5. What happens to someone in a memory care facility if they run out of money? We're in California. I have been getting conflicting messages on this question.