Do you need to send a itemized list or damaged and unpaid rent to your tenant after they move out if they were evicted and have a judgement from the courts against them? 

If you requested a showing and couldn't get in, it could be due to your realtor.If the seller/seller's realtor is hostile from the start, it could be due to your realtor.The realtor reflects the competency and judgement of the buyer. 

As a new Texas Landlord, I have learned so much going through a successful eviction process, I did not know I had to do this last part, Abstract of Judgement, to show this debt on the tenant's credit report.

If they don't pay I can sue them in small claims and get a judgement, will probably cost a few hundred dollars in court costs. 

The basic background check is through smart move and they have an option for the prospective tenant to pay and have an add on option for judgements and liens search.

Then when things are lifted , file for eviction against both and get a judgement 

The answers to this would determine my next steps.Yes not being able to verify the info makes it difficult.I did just talk to one attorney and they did suggest the best thing is to start the eviction process - asking for just possession, and not a money judgement (get back rent owed and cost of filing), would make it easier - although he's not quite sure how the court would handle the tenant not being mentally capable (just found out from the fiance today that - supposedly - he's out of the coma but is "sleep-awake" and has no clue what's going on, and is paralyzed on the right side of his body (again, can't confirm anything).So the fiance has (confirmed) already moved out with the kids and is living with an ex-BF (one of the fathers of her kids) and no, she is not on the lease (another lesson learned). 

If your sued from inside the LLC and you have a mortgage on the properties, they will have to sue, win, get a judgement, then foreclose on the individual properties.  

I failed to address your other concern regarding future judgements, liens, and etc.

Small Claims Court (the tenant will most likely receive a judgement to follow them to pay their fees to you, although this will take awhile to work, there is still a chance in the future you will receive a check in the mail - since it will catch up to them) In addition you have.. 3.