Great list 
My quick answers for now.
A lot of this type of stuff is very individual trial and error.
Chaffing: I find the best thing is to figure out what clothes, shoes, tack work best and don’t rub far in advance. I personally like tech fabrics for my own clothes, I ride in trail running shoes and use stirrup cages and I have real sheepskin on my saddles to cover both the seat and the stirrup leathers. Staying as dry as possible is important too. My favorite product for chaffing is something called Salty Britches.
Chapstick- I only use it in winter but I also live in an area where the humidity is ridiculous. I know a lot of riders carry it in an easy to reach pommel bag type spot
Electolytes- as far a horses go, you kind of have to figure out what works for each horse and it can get pretty complicated. My Morgans I have to elyte very heavily when its warm out. I like EnduraMax. I do doctor it up a bit. I usually add something to buffer a bit like ProCMC and something to make it taste good like baby food carrots or date syrup. Things like NoSalt or CMPK can be added/ given if your horse’s pulse is hanging or they seem a little muscle tight. Timing is also important but very individualized. For instance if you have a horse that really dislikes being electrolyted, giving them right before going into the vet check might be a bad idea because it might spike their heart rate.
I do carry a sponge on my saddle. The main thing is PRACTICE before hand. I’ve seen some wrecks that came from swinging a sponge around when a horse had never had it done before. Sponging along the trail when the weather calls for it can really help your horse stay cool.
People water- I use a bottle holder on my saddle for endurance or CTR and the backpack style if I’m doing ride and tie. I prefer the water on my saddle. I usually have two bottles and I prefer a bottle that has a sport top so I don’t have to deal with a lid. Anything left in my bottles at the end of the loop get squirted over my horse’s neck/ shoulders during the last 1/4 mile into camp to help with cooling
Hoof hardner. I don’t generally use anything other than Durasole occasionally. My Morgans have feet like rocks. I do know several people who swear by Hoof Armor
Human fitness- whatever you need to be able to stay balanced and comfortable in the saddle for however many hours you are doing and run your horse for the vet. I do a lot of strength training, hiking and trail running. But I also know people who just wing it for the shorter distances and then put up with the soreness for a couple days afterwards lol
Pulse- I use a stethoscope (some people use a digital one) placed just behind the left elbow and count for 15 seconds and multiply by 4.
Vet check- you are unmounted for vet checks, most of the time untacked. Sometimes vets may tell you at the pre-ride meeting that you can leave tack on for a vet check like if the weather is cold or you are doing a short vet check (called a gate and go)