First of all this isn't a 'Studio Apartment', rather, this is a room in the host's mother's apartment. It is misleading on part of the Host & AirBnB as well to enlist this as an 'entire apartment'.
However, the room does have a gas stove and a sink.
Nothing is actually good about this place, the sofa bed is so uncomfortable that you'll wake up tired. The pillows are a clump of old foam pieces. The blanket stinks. The bathroom stinks. Water doesn't drain. There's grime and mould around the basin. The window blinds don't work. There are mosquitoes galore.
It isn't too far from the Duomo, then no place in Florence is. It is a very small city and the Duomo is walkable from almost everywhere.
Don't waste your money on this dump, get a hostel, it would offer more comfort and value.