If it’s a safety issue, I’ll of course make sure the premises are as safe as they were before any required maintenance was done, but she is now suggesting that if I don’t reimburse her for those specific anchors, I am violating fair housing laws for familial status and/or tenants rights regarding not incurring costs for required repairs.

Your ONLY cost in a rental is the cash you come up with. 

She called it a cash offer, but included a letter from her hard money or private lender (same thing, really) stating the lender is good to go with the deal, the lender has plenty of liquid cash, the buyer has his 20% down payment and cash for closing costs, and there is no financing contingency.3.

If you sold the quad there are costs involved, and then you have to find somewhere else to live.

In all honesty, this rental increase in a depressed area makes me wary that future increases will be more unreasonable and more extreme, and I should "get while the gettin's good."

For example it might cost $3,000 to repaint an apartment and that is a charge for the landlord, but to repaint the wall after you left it with patches is about $200. 

If it's beyond normal, do I just charge what it costs to fix it or do I have to discount the cost for "normal wear and tear"?

How much would something like this cost?

.: @Michael Tompkins get a HELOC I suppose a HELOC makes more sense than doing a cash out refinance since I would keep my current interest rate and wouldn't have to pay closing costs.

Rust Belt (like you are looking it) is OK but pretty economically depressed.