First, the views from the Terrace are stunning, you are very close to the Duomo, and we greatly enjoyed our time in Florence and this apartment. With a few caveats, we would recommend this to others and stay there again.
The best description of this apartment is "quirky!". Don't take the elevator (if it works) to the fourth floor, you only take it to the 3rd and then go up steps to the 4th floor and the door. Then more narrow steps up to a small landing (left to the small bedroom and bath) and right (via very shallow steps) to the living area/kitchen. I'm 6'2" and I'm ducking through the various doorways.
The main kitchen area is about 4 square feet, with a sink on one side and stove on the other. The ceiling height in the kitchen is about 5'10". Just outside of this area is "normal" ceiling height and a small refrigerator.
Once you get used to these quirks, you'll be fine and love the views.