Constructive criticism.... a helmet?? Yes, I am a mother!
Heels down, feet forward, unless you're actively wanting to yield his HQ or such. And practice riding more with your seat & less with your reins. If he's doing as you ask, loosen the reins.
Groundwork? Yes, very good idea. Depends what you want out of it & what you & he already know as to where you'd start. So if you don't know what he knows, I'd start at the very beginning.
I think just hanging out with your horse is valuable too - as Saddle suggests, you can take a book or something else, to do in his presence, or you can just be there & ask nothing of him.
As for doing 'stuff' on the ground with him to further your training, I think the principles of Parelli's '7 Games'(do they still teach this the same? Maybe go for older stuff...) is invaluable for both horse & human to understand. It is the same sort of approach as CA(I think differences between them are mostly about personality). It will give you the basic foundation to do whatever you want with him on the ground or under saddle... or harness.
As for liberty, get really good at everything else first, get him *reliably* able to be ridden without having to touch your reins before considering doing away with them... in a controlled environment... wearing a helmet.