For example, say I want to cast demiplane and make it zero gravity. Can I do this? The rules do not say anything about the demiplane's gravity so this seems like it could be valid but I am not sure.
It's total DM discretion, but yes, you could. The only direct thing that says about its main, base rules is that it has to be wood or stone, it's empty when created, 30 ft in all directions, and only allows up to Medium creatures to pass through the door to it without having to make a skill check.
[from the Basic Rules, pg. 231]
The door is large enough to allow Medium creatures to pass through unhindered. When opened, the door leads to a demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone.
Other than that, it's fair game as long as the DM allows you to do that.
Possibly to any extent (including zero-gravity), possibly to very little
The demiplane spell only specifies a handful of rules:
a demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone
Anything beyond this is open to interpretation by you and your GM. There are details on the limitations and qualities of demiplanes in the Player's Handbook Appendix C, "The Planes of Existence":
Demiplanes are small extradimensional spaces with their own unique rules. They are pieces of reality that don’t seem to fit anywhere else... They may exist naturally, as a fold of existing reality that has been pinched off from the rest of the multiverse, or as a baby universe growing in power...
With so little details, it will be entirely GM dependent what the limits of your particular demiplane are.