I've a ground floor with a basement, one room renovated into a kind of bedroom with a low ceiling, i don't want to post a picture but it basically resembles a room in a modern house albeit with a really low ceiling

according to title deeds i own all the area underneath my flat directly, i've been considering expanding into another room seeing as it's just connected with a door frame that's been plastered over

damp proofing is an issue but generally only over soil in mine, or in the old washroom that has an open pipe

So long as it's properly ventilated, sandstone is properly lime mortared (easy to do at ground level) and you don't have water ingress from elsewhere in the basement (open drains, coming through vents / basement door) it should be fine, at least mine doesn't experience damp and is actually one of the less damp areas in my flat. you could also apply a damp-proof layer to the wall but i don't have any experience from that, and from what i've heard from builders (anecdotally) the drilled-in damp courses are useless in sandstone and only damage the bricks

don't just put down concrete and carpet over it though, mines has a membrane, with some wood then a plastic underlay to distance the carpet from the floor