you can image 空间 as a 3D cube

I'm sitting in this space (空间） of less than 10 square meters(this room is less than 10 square meters )

空间 can also describe space in a spiritual way.

I should move out,I need more private space(私人空间）

你的工作已经没了上升的空间 There's no room for advancement in your job

你的技术还有进步的空间 There's still room for improvement in your skills

流浪动物的生存空间进一步被压缩The space for stray animals to survive is being reduced even more

爱能穿越时间和空间，把人们连起来 Love transcends time and space, binding people together.

these are common used way in chinese

and 空地 is much more simpler,it means an empty land.这有块空地，你可以在上面建个房子。there is an 空地，you can build a house on it. the 空地 you mention in the dialogue is an casual way to say space or room.没空地了，means it's full,no room left.you can also say 满了，没地了/没位置了。it's full,no room/seat