Someone will need to come out and do a basic inspection for safety, but it's not a big ordeal. 

The answer will be in the purpose of the lock.If it is to keep others out, the double key is best.If that lock will stay on the door after renting, then it could be a considered a safety hazard against someone getting out quickly if they needed to so a knob latch on the inside is best after renting.I prefer the latch option at all times, because once inside and working on the property, I dont usually lock the doors anyways while I am there.

Honestly, respecting your tenant's right to safety and privacy is the better course of action.

Buy with a margin of safety, buy with a good cash flow.  

It depends on a few factors but the most important one is probably is it worth it financially speaking and in terms of safety.

What is the best solution to upgrade the property without my parents having to sell before things become a safety issue? 

According to Neighborhood Scout McAllen scores a 13 (out of 100) for safety.  

If I can figure out how to get my bike on the MARC, I'd rather ride around on the bike, as there are somethings you don't notice from the safety of your car.

The information on zillow app and ability to see preliminary credit report narrows the tours to only qualified potential applicants, and I know at least some information about them, which is  especially helpful for my personal safety as a woman showing property to "strangers".Prior to using zillow app to pre-screen, I lost SO much time touring ineligible or underqualified applicants & people who grossly misrepresented their situation.

Always operate with a margin of safety to maintain profitability.