Can they have a beverage of adult nature, or that also will have to be approved by you. 

Adult conversation is going on.

Lastly, 2 of the 4 adults living in the house only get paid cash, and do not have a bank account.  

For properties that are having non-emergency work done, especially if it is something for the convenience of the tenant, and the tenants are highly functional adults, I am fine with having the contractor make arrangements with the tenant - especially when there's not a "nail-down" time, like often happens with HVAC.

For Tenant, if they are interested in signing a lease: 1.Fill out preliminary application.2.Verify application for 3 times monthly rent income, pay stubs, no felony, no evictions, at least 1 year on job.3.Query all adult names in state Courts Online system.4.Query Facebook.5.Query County Assessor page for properties in their name (foreclosure?)

In my jurisdiction it is common practice for the eviction complaint to list all known adults living in the rental by name and then "All Other Occupants" to get good service of process on anyone else who may be living there. 

Two adults, three kids and three dogs in an 2/1 is hard on a place over 4 years.  

While you're not directly responsible for the adults you rent to, as a landlord you are responsible to reduce risk in the home and care for the safety of your tenants. 

I am renting to a young male adult who checked all the boxes during the application process.

There are plenty of adults in the world today whose parents spent almost every waking moment making sure they had all they wanted(wanted not needed!)