1. How do you handle resupply of things like your first aid kit and repair items? Do you mail yourself some more ibuprofen and krazy-glue half-way through the hike or some other interval and if you don't need, you just leave in the hiker box?
If you think about your JMT hike as simply a few of your three day hikes back to back it will help you plan. What you bring in your first aid kit will be plenty for the whole trip.. trust me. As for Vitamin I (Ibuprophen) I usually bring 25 tablets and that lasts me an entire thru hike of 4 months. I can't imagine you would need more than 1 tube of superglue for the JMT. Actually my entire first aid kit is vitamin I, a foot of duct tape, 1 dose of Metronidazole antibiotic(Flagyl), and a few benedryl tablets. This is not meant to discourage you from bringing whatever you feel is neccesary to be safe. It's hard for me to give this kind of advice but I honestly have to say that as a thru hiker I have never needed more. Maybe someday I will.
2. How much soap do I need for 5 days at a time? I usually take the whole bottle and don't worry about it. I'm taking Roger's advice and plan on keeping my bum clean. Also, really contemplating foregoing TP for a bidet squeeze bottle, so I'll need more soap!
I don't use soap. I carry a 1 ounce bottle of Purell or similar hand sanitizer. The purell doubles as fire starter in an emergency as well. (burns like napalm!)
I also don't use TP. I use natural materials and clean up with water well away from water sources and places people camp. However I realize i am in the extreme minority. Whatever you choose be sure to wash your hands and keep your fingernails clean ,even if you don't normally do this at home, after pooping. Believe it or not two different women taught me the "bidet" technique to avoid the use of TP in the back country. Supposedly it is an NOLS technique. I do it because wiping never gets me as clean as washing.
3. Any other thru-hike advice? I'm thinking a calling card is a good idea? How much cash makes sense?
The calling card is great. I always carry one. The pay phones will rip you off for 30 units right off the bat but sometimes you can find a sympathetic buisiness owner and use their phone with your card to get around the surcharges. I would carry a few hundered bucks cash. When ever you reach the road to resupply, ALWAYS remove your cash, ID, and ATM card from your pack and keep it on your body during the hitch to town. Also always keep these items on you in town or at hostels.
I find that buying food in town for resupply makes the most sense. they sell candy bars, tortillas, cheese, and peanut butter everywhere so theres really no need to mail these things to yourself. Usually it's about $10 per day for trail food at a resupply. So a 5 day stretch would be about $50 at a convenience store or supermarket.
I guess my best piece of advice is; Don't think of the hike as 200+ miles. It's simply walking each day. The miles will add up quicker than you think.
If you are already planning on a mid-point resupply like Vermillion Valley resort then it's no different than two slightly longer hikes than you are already use to. That way you aren't packing food, band aids, and soap for 12 days.. you are packing those things for two hikes of six days each.
Trust me, you will be able to find any supplies you need in:
Independence(via kearsarge pass, gas station has large hiker resupply section)
Muir Trail Ranch(sometimes there is a hiker box or you can send a 5 gallon resupply bucket but it's 50 bucks),
Vermillion Valley(hiker store,meals, hiker box, you can also send a box here),
Reds Meadow(limited store or you can take the bus to mammoth which is an awesome town),
Tuolumne Meadows(decent store).