I purchased a home with a Florida room addition. The floor is a concrete slab at ground level. From the house I have to walk down three steps to enter. Can I convert it to living space, add a raised floor to the same elevation as the rest of the house, add heat and raise doors and windows?
Jim, the nice thing about remodeling is that just about anything is possible -- it's usually just a matter of whether the project is worth the time, effort, and cost. Of course, that's something that only you as the homeowner can decide.
It's difficult to provide an accurate list of all the issues that should be considered without being able to actually see your Florida room. However, one thing that jumps out is the major change in elevation between the room and the rest of your home. While stair riser heights can vary, with three steps the difference in room heights must be close to two feet and that's a major change in elevation.
You're correct in the assumption that the window and door openings would need to be changed, but there's also a good chance that the ceiling may also require adjustment. A ceiling can normally be raised several inches or even a foot without affecting the structural framing of the roof, but two feet is definitely pushing the envelope. The roof framing where the Florida room ties into the main portion of the home could need to be altered and that can turn into a major project.
Also, don't forget that the height difference is still going to exist -- it's just being moved to a different spot. I'm assuming that the Florida room slab is about four inches above the exterior grade of your yard - that will increase to about two feet when you make the change. It may not be an issue for your family, but it should still be considered.
As far as how to raise the floor, my suggestion would be to install a floor joist system. The area under the new floor would essentially become similar to a crawl space. Knee walls could be framed at the perimeter of the room to support the joists or you may be able to attach ledger boards to the existing framing.
You should get an architect involved in the project as they will need to address the possible change in the roof framing. They can also provide the best option for installing the floor joists and you'll probably need their drawings for the building permit.
While it's entirely your decision, in my opinion the project could involve a lot of work and cost just to move three steps to the other side of your Florida room. I would finish the room at its existing elevation.