(Whether this makes financial sense is probably a discussion for another post) Should I insist on meeting prospective tenants face to face before agreeing to lease to them?

As a buyer I would insist on #1....too much risk for the buyer otherwise. 

If anything could get further damaged you may wish to insist they get rid of th ecat.

Most of them insist on 5 days (At least in my experience and my investors'.So far, I bought four houses cash and I've been to non of the inspections.

The insist that once the account is paid off in FULL, those funds MUST go to the original borrowers.

If you insist, then ask What are the condition of the reserves?

Real estate agents sometimes insist that a bedroom contain a closet, but that may not be an actual legal or code requirement in your area. 

My favorites are the ads where the seller insists on a "cash only" deal, because they need to sell quickly, but their asking is either at market or only slightly below that  And then the ad sits there for a few months. 

I insisted on using a local title company.

Just because they say its okay over the phone doesn't mean they won't deny you when it comes time to run it through an underwriter.I had a broker get upset with me because I insisted she not commit to an appraisal (cost of $450), before clearing underwriting, unless she were going to foot the bill if I was denied.