I've never carried a hatchet nor a saw, but have considered this question lately, partly due to developing a taste for fresh meat.

(That is, meat purchased at retail, and cooked on wood fire, though I've also considered on-site grey squirrels, and have experimented with this in home kitchen. Results were somewhat encouraging.)

Most of my camping is in areas of hardwood forest. Not sure how this works in coniferous zones. Might be yucky flavor due to stinky sap. Also, the reds, I hear, are bad.

Also partly due to a lot of my camping getting done in middling winter weather, when temps are coldish..(say 20s-30s F.).. but not so cold that a smallish fire becomes useless as temporary warming device.

So I've lately considered the saw/hatchet question, and have concluded, very tentatively, that a very light saw is lighter and safer, and perhaps more effective, than hatchet.

Certainly if cutting weight rather than wood is a priority, I'd ditch the saw or hatchet. Totally. Nix!!

Also, I imagine it's fair to assume that your 1-degree bag is rated in centigrade, which would be an optimal item for the region you're referring to in summer conditions.

Phat's on top of all of these questions, though I think sleeping in a hammock sounds very weird, uncomfortable and extremely dangerous and possibly even a problem for society.