The heat went off in the winter while the house was unoccupied, we had a week of record lows and the pipes froze and burst in the house everywhere.

Fellow and spearfisher here in Miami!

It has at least one ceiling vent that I understand is connected to the rest of the central heat and air system.

In Cincinnati, it is common to have heat and water paid by LL in older properties, since it is one gas meter feeding a single boiler to heat the radiators in the various units.That being said, you are generally talking about expense conscious tenants in that C-ish range. 

Do the tenants pay for heat?

Miami, Fl.

I also asked for copies of electric, heat, and water bills.

A/C, electric heat, electric HW, any other big-ticket items?

As others have mentioned, check with your local building department, but most municipalities require 2 points of egress, a heat source, a closet and a minimum ceiling height of 7 ft. 

Does anyone know how much (roughly) it is to convert oil to gas heat on. 2,500 sq. ft. duplex?