Yes, contact with peanut can cause reactions.
If you leave little dabs of peanut on a tabletop, there are people that will get a rash, or hives, or even a fullblown allergic reaction from the micrograms they pick up when they touch he table after you.
There are other alergens just as bad, like shellfish or tree nut.
Yes. Touching the cookie in the food fight bought him 24 hours in the hospital, and this was not one of his severe reactions.
Just walking into one of those bars that have buckets of peanuts on the counter can kill a highly-allergic person. Just breathing the dust. I got in an argument with an anti-smoking zealot one time about this - he admitted that while he couldn't stand to walk into a smoky bar, at least he wouldn't drop right down dead, the way a peanut-allergic person would in a peanut bar.