For example, HAI in one of the markets I'm looking at is 245 . is this a red flag?

Anything that I should focus on from the start, or instant red flags that are show stoppers?

I think it is a red flag that she wants to rent your place 3 months ahead of time, unless you are in a very hot market. 

You'll notice as you go South and you research Red States laws are more in favor for Landlords and Property Taxes are more manageable..  

If a prospective tenant is in a rush to move, usually it's a red flag unless they tell you upfront why they need to move.

That is a red flag to me. 

3 red flags:1. 

For example, HAI in one of the markets I'm looking at is 245 . is this a red flag?

Even caught red handed you would be way ahead and wouldn't have to go through all their non sense permitting process and very likely wouldn't be fined if you retroactively comply with their inquiries.

A few years ago I helped my (retired) parents buy their most recent house by directly giving them a $100k cash down payment, and they would like to leave the house to me when they pass in thanks for the assistance (it ended up helping keep their mortgage extremely low since they are on a fixed income).They are very worried that it will somehow get caught up in probate or red tape when they pass even if my name is spelled out in the will, and wanted to see about just adding me to the title or something so that there is a seamless transition without any hassle.