The civilian labor force increased from 1,265k to 1,335k yoy.

You are correct about the VA loan, they do want you to have some length of service time after the loan is closed, or you have civilian employment. 

While they may be understandably creeped out by the thought of rat dookey sitting in the ceiling, if the law does not require it and the pest control technician indicated there's no threat to inhabitants, there seems to be no value in spending thousands of dollars just for peace of mind.  

I don’t know 100% if the property is inhabitable, it is just appearing that way in the photos (I am trying to get in touch with the listing agent). 

But everything I read online tells me that a property cannot be inhabited or rented out if there is no current Certificate of Occupancy.

Snap traps are humane generally and generally do a great job getting rid of pests - you have to find the bait that works best...I wish that humans would think about how their actions harm other inhabitants of this world and treat all living beings with respect - even if you must kill them - do it humanely. 

I am currently in the military working on transitioning back into civilian life and preparing to move to Dallas-Fort Worth area in a couple of months.

The unit I plan to live in is inhabited by a man who has lived there for 17 years with no lease.

My question: is the damage sufficient enough to prevent the unit being inhabitable or hurt your success in renting it out? 

The foreclosure just hit the three year mark and the property was not inhabitable at the time of the hard money.