I think he does have a lease with the tenants, but he said the realtor contract is only for the realtor to lock in the client for a specific period.

A door lock doesn't function, four cracked windows, a broken door handle...those sound like issues the PM should have found during the inspection.When you get a lot of repair requests from a new tenant and they seem to be legit, I would recommend they spend a week or two getting settled, write down all the issues they come across, then send your contractor to handle everything at once.

So, changing locks, shutting off utilities, removing the front door entirely, etc etc.

If he chooses to stay, review his finances to verify he can afford the new rate, then lock him in with a new lease.If he can't/won't accept the rent increase, give him 60 days to find a new place.

I practice situation awareness and keep my stuff locked down to minimize the risk I'll be a victim.

If I was a renter today, I'd be doing everything I can to get the longest lease possible, 5yr, 10yr+ to lock in because this is an enduring upward pressure on rent's that only has 1 release valve, price ascension. 

Finding a reliable property management company in Texas will be crucial.

Is Rently designed for showings with no one there (since it comes with lock box) while ShowMojo is designed just to schedule showings?  

My family member does have an agent in mind but nothing is locked in yet so I want to help him with his due diligence. 

She is currently locked into a lease, but she will be $900 short on rent this month and she says it is getting harder to pay every month.She has never been late or given issues before  she takes GREAT care of the property.