Alright, I'll answer this one since no one else seems to want to do so. I resupplied almost completely on trail this summer on the PCT. This is far superior to mail drops from home. If I hike the AT this upcoming summer, I will do so again.
I set no budget for my hike, so I can't comment on point 1. For the first 50 days or so of my hike, I would generally put in about 160 miles per week. I would carry about 3 lbs of food per day to fuel me. The last 55 days or so, I would generally cover 200-240 miles a week. Strangely, my appetite decreased in the last month I was on trail. The point is, my food consumation was higher than most people on the AT, due to putting in longer days with more miles and elevation gain. I would generally spend about $10-12 a day on food. Sometimes a little more, sometimes a little less. A standard, 3-days-and-a-morning (roughly 100 miles) stretch between resupply points would usually cost my around $35 or $40.
A lot of places on the PCT where you can resupply are really, really small towns or resorts or state parks. This makes the cost of food higher, but you still save money because of the postage savings.
Definitely resupply from the trail. If there is a place where you are assured you cannot resupply, you probably still can. However, if it makes you feel more comfortable, send the mail drops from the trail itself. That is, buy food in town, put it in a priority box, and send it to yourself. The advantages are: 1) Postage will be less than sending from home, 2) You'll actually have a realisitic idea of how much food you need, 3) You'll have some idea of what you really want to eat at that time.