The slab has probably been there for ages and will never move. How old is the house/shed? Cracks won't affect it too much. From the pics, it 's a fairly big slab.
Removing it will be labour intensive. Jack hammer (sledge hammer) it to pieces, get the pieces to the front (down that retaining wall ugh...) and dispose of it (a few trailer loads or a skip). Then dig out new footings/slab or level and put down crushed rock or whatever and put a new shed in it's place. And a small retaining wall depending on how much it's been lowered. It would be an expensive and time consuming excercise for not much gain. Or put in something larger if you want more space. But you're still left with a shed you can see. If you use it and it's an ok size, I would keep it and just screen it as mentioned above.
Your neighbours will love you for that!!!