I'm guessing this is the garden of a ground floor apartment where there is a 2 storey duplex above it.
The OMC will of course own it as if they didn't, you could build and extension / add a garden room etc. So to ensure it is used as a garden, you have sole rights of use of the space as a garden and that is legally protected.
Round-up is superb for getting rid of weeds. Some don't like it as there are very faint suggestions it can be harmful, but even then that's on prolonged use.
Grass needs very little soil depth to grow nicely, so I'd kill off everything, get a couple of ton bags of topsoil, some plastic sheeting and a couple of students. Get them to wheelbarrow the soil through the house (on the plastic sheeting) level it out, plant grass, maybe a couple of miniature trees and enjoy a simple easy to maintain garden.
Hint - a half sized coal scuttle is great at getting soil/gravel out of a ton bag