future remodel idea: running power to a shed, converting old storage room to livable space

With our growing family and wanting to be able to have guests/family stay over, I want to be able to utilize the current space I have at my mom. The only thing I would to add would be a shed to the backyard and run power to it which would house my yard equipment/power tools. The room I want to remodel within our home would be a roughly 12x12 room that has our water heater in it. This room is behind our half bath so it would be ideal to have a guest with bathroom access vs. having to build another building and run plumbing to it.

My main questions:

What would be the difficulty of running power to it, given the surrounding area is 10x10 slabs?

Can I actually use a room with a gas water heater as a living space even if I aesthetically cover up the heater and pipes? I say living space but this would mostly be an office/guest room, likely with some type of fold out couch that turns into a bed. I would have to add either window unit or mini split to the room since the central air does not go to this room.