I'll give my view, but i'm sure gasman will be back later too.
1) Unless you've got water-based UFH already, considering it for such a small area is a non-starter. If you are talking about electric mat that is laid below the floor-tiles, this gives a nice warm feeling on the feet, but you must be prepared to dig down to install at least 100m of Celotex or similar insulation - otherwise you will lose a lot of heat through the floor. Personally I would put a towel radiator in that doubles as a space heat source.
2) It is less labour-intensive to install an electric shower but more expensive to run. With an electric shower you only have to run the cold supply to the room. You are going to need a qualified electrician in any event, assuming you want some lighting modifications in there.
3) You are going to have to dig down anyway to allow the shower drain system to be worked out - and you really need the shower to be lower than the floor adjacent to it - or any escaping water runs in the wrong direction - away from the drain.