Real estate is always local, so these numbers may not be at all applicable in your market.

We never signed any document's other than the application.

Only the people over 18 are the tenants, but state that only the following people have the right to occupy and list all names, which should be listed on the application.  

Applicant gives me a wrong name/number - easy: Declined.2.

(that I never read) is applicable to Billy Bob's private mortgage to you.

Besides building credit and saving which I still highly advise, I would say the second best option would be to find a co-signer or co-applicant for the property.

In terms of due diligence, for example, for an acquisition FHA under Section 223(f) you would be looking at an Appraisal, Phase I Environmental Assessment, Capital Needs Assessment (depending on the age of the property it might include Asbestos and Lead Paint testing) and Radon testing (where applicable).

Make them fill out an application as well and put their name on the lease. 2) Since we are going to live on another side of the property, should I tell them I'm the "manager" or their landlord? 

However, my father will arrive tomorrow and speak with the mortgage department with application in hand.

The bank that owns this property is a small local bank and has offered 100% financing and some help with funds for rehab depending on my credit application.