I ALWAYS require MINIMUM 3X rents in gross household income, no exceptions other than pre-paid for FULL lease term (yes, I lease this way, not theory).

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Your ineptitude may amplify your losses:(You're also jumping to assumptions.We've had out-of-the-county investors that we could NOT legally send funds to because they hadn't supplied us with the IRS required documents - and they didn't respond to our numerous communications to get them.Once we obtained the proper documents, we sent them their funds - by the way, we did send monthly Owner Statements, so they had the info to see what was going on with their portfolio.So, that brings up another question - what information have they been sending you and when have they been communicating?

What if you require more rehab $'s than originally estimated?

Our property doesn't meet the zoning requirements, so the decision has been made for us. 

All those things require maintenance. 

In addition to this what else can I do to protect myself and ensure that they don't take anything more than is required from that security deposit?

If you ask the manager to justify a fee and he starts hemming and hawing, move on or require them to remove the fee.

Although a DSCR is lenient on your personal income, they will still require a relatively clean appraisal.

If smoking isn't a requirement, it isn't a requirement.