Hi.
I started with about 6 inches of water, then as I looked further into this site I ended up filling up to the top. My two do use all their space for lurking in plants , swimming , feeding etc.
With regards to a lid, I made one as I have stinky cats and didn't want to risk the axolotl coming to a sticky end..but mainly if they are startled suddenly ( only seen it once) they do go like the clappers and tend to leap out of the water...which could be life threatening for them. I used a quite fine ( small holed) one rather than solid as I believe they need a good air flow......having said all this one cat has taken to lying on top of this until he is kicked out side. Now have to modify to keep the cat off!