While it might feel like an extra charge to tenants, these packages often provide value that indirectly benefits the property owner as well—like reduced maintenance calls or ensuring the property is better protected.In my experience managing a large portfolio of properties, these fees are becoming more common due to the thin margins in property management.

How is PM charging you if the agreement is over?

If it turns out that the tenant clogged the drain, we give them one warning and after that we charge them.

Should I charge her a prorated amount of the original rent or the increased month-to-month rent for January?

Quote from @Aaron Wolman: Yes, these charges are fair.

The pet fee or deposit for the move in of 2 cats (you did charge one, I hope) should have just about covered the extra anyway.

They should have also gotten approval from you before charging and doing repairs.

The FBI’s Financial Crimes Unit investigates these matters for filing of charges on Equity Skimming violations.

I was charged a year’s membership. 

The first few times, I didn't charge a late fee.