@Jamie Dupont Well you aren't alone in having struggles in the early going in real estate investing. We've all had them. Think of it as starting a business, no one who has done so has had things go perfectly. And while you may be experiencing worse than average issues here, if you can stem the tide for the time being financial you will come out of the other side learning a lot and you will be ok.
Without being in the situation it's tough to say for sure what exactly the PM should've done. It could be possible they tried to collect rent, and with the tenant knowing she's leaving, chose to not pay. And for you to recover rent at that point wouldn't be worth the hassle of suing. The good news is that this person is out and you can do the repairs and move on which is a better situation than some people end up in.
When you select the next tenant I would certainly ensure that you have your eyes on the applications that are coming in, and ask that you are involved in the decision making process. 3x income, clean credit and background checks should be a minimum for approval, even if it takes a month or so to find someone.