My monthly payments (mortgage, insurance, taxes) are roughly $3,600, leaving me netting about $4,600/month.I have four years left until military retirement, after which I’ll have a pension, some disability income, and rental income from this property.

For example, we need proof of renters insurance and proof they put electricity in their name.So, it seems odd that you are accepted but they keep wanting more information. 

You want this to be your backup plan if things take longer than anticipated, you do not want to dip into personal credit cards so i would use a heloc to help with down payment but try to keep a nice available balance on a heloc as your insurance policy. 

You'll want the rents to at least cover the monthly principal, interest, taxes and insurance (and HOA if there is one).

That's easy compared to trying to fight and erroneous $13k water bill (a real issue we had) or an insurance policy tripling (that too).

Helps with your debt to income, better opportunities at cash flow, and typically requires less down to purchase.In regards to challenges, I usually build in an extra 10-15% to deal with things that I can't see behind the walls, including dry rot, electrical or plumbing issues, etc.

You want an investment that pays for itself, including mortgage, taxes, insurance, maintenance, and even some money set aside for a reserve to cover vacancies and capital expenditures.

Furnaces break roofs need replaced and plumbing needs repaired.

Taxes and insurance will be another $400+.

You should allow a 1-2 Weeks for the appraisal, and 1-2 weeks for title and insurance.