That is your homework - and you should ask for proof or ask other owners what they remember about all of this.

To make a long story short, they went to court and lost because they had no proof of payments being made.

Legal entities aren't a fool proof way to protect your personal assets.Always carry appropriate and adequate insurance.

In VT, you can still sue in Superior court if the amount is less than $5k, although they encourage you to use small claims for that.Just make sure everything is thoroughly documented and you have proof you sent the deposit return within 14 days after the end of the lease.  

@Kon Zel thanks for the reply, I don’t think I am eligible to be put on the mortgage as I don’t have Any proof of income from the past two years.

I would either send certified mail or heavily document for the proof you sent it.Just as a side - I wouldn't use a lease that says they are responsible until someone else moves in, just a lease break fee of 1 or 2 months and move on from them. 

Also, what documents would be needed to show proof of primary residency?

I opened a bank account at Bank Of America and they know what my salary is based on what I told them, but never showed any proof of that and it's approximately 80,000$ a year .

I also would make your final closing depending on both property inspection reports (consider this a good investment expense if go for these higher than normal comps asking prices), consider adding a depending clause on getting a current appraisal value as part of your offering contract, and proof of section 8 passed standards for both properties (this is in my opinion you need because the seller is increasing the values based on these properties being at section 8 standards).

HUDs guidance memo does state if the disability is not readily apparent you may request proof from a "physician, psychiatrist, social worker, or a mental health professional."