1. you could wait and see if anything chews thru the CW, or put HC all the way now.
2. If you get standing water now, best dig some trenches to alleviate that, both outside run and inside(if necessary).
I don't think the gravel is a good addition, wood chippings and other dry plant material will do the trick.
3. They can find a place where litter is not so deep, or you can make one, to bathe in.
4. Use pressure treated lumber in those areas.
5. Pneumatic staples should be good, 3/4"...make sure edges are well pinned down, at least 2 squares from edge, and HC is flat and taut across expanses.