Repair and maybe reduce size of concrete slab?

We have a detached garage that is currently 12x18'. The concrete slab it sits on is uneven - whenever we get a big rain or snowmelt in the spring, about half of it floods with up to an inch of water.

I'm looking at repairing or replacing the garage itself, as the bottom boards are a bit rotted out. I'm considering a slightly smaller shed to give more room in the backyard - I found one I like that is 10x16'. This would make it no longer technically a "garage", I suppose, but we really never use it for that anyway. It's at the end of our private drive in mid-town Toronto, but the driveway is extremely narrow - there would be just a few inches clearance on either side of the car mirrors when driving between the two houses, so you have to be a pretty precision driver (we have parked up to six cars using the entire driveway length, but you have to think really skinny and squeeze out between the buildings!).

So, my questions:

- Is it possible to just pour new concrete on top of the existing concrete to level and/or raise the floor to prevent flooding?

- Is it possible to reduce the footprint by cutting the edges if I choose a smaller shed?

- Is it better for home values in Toronto to keep something I can technically call a "garage", or does it matter if it's just a shed? (Especially considering it would be a nicer, newer shed?)

Thanks so much for your help!!