In many ways I think the last two items are more personal preference. 

It is listed as a single rent value but I believe they also rent by the room. 

I have a list of PM's, contractors and lenders that have helped several of my investors when acquiring properties in Cleveland.

I jumped on the MLS just now and see one condo in Miami Gardens for $125,000 and the listing claims that the current tenant is paying $1200 per month.

All of these tools allow you to pull lists. 

Ugh.Prop management in my area is 8 -10% Plus half of the first months rent.I'd get some firm numbers from locals on prop management and if there is a wait list for him to be able to rent it. 

Example.Property listed on the MLS for $200K.

Does anyone list particular debt limits (like, "no debt in excess of $1000 that isn't in a payment plan") as part of their screening criteria?

Being listed on the bank account?

There is a list of state licensed contractors in the state.