You need at least 2" of water in the shallowest part of the pool to keep the liner 'set'.

3" would probably be a better level, just in case...

No need to cover, as long as no tree branches, etc. might come crashing in and rip the liner.

I think you're doing the correct thing in keeping the liner in place to prevent any (more) damage to the floor - however, given the fact that you had some leaks, retrowelling the floor will probably be necessary before the new liner is installed next spring