1. He/she can be held for as long as you can keep him/her friendly! We still pick up our three year old chickens from time to time, though only some of them will let us without running away first.
2. He/she should start walking normally within twelve hours, although it will be common for the chick to take frequent naps. Our chicks started hatching about three days ago (and some are still popping out) and they are all off and on active.
3. The feathers should dry within two or three hours. From there, more feathers will come in as often as the shorter ones fall off. Before the first 24 hours are done, it should be all fluffed up.
4. When they're young, the bright light doesn't affect their sleep as strongly. After about a week, we start using a more red-ish light; they can sleep with it on them easier, although I'm not sure if it's a ceramic heating light. I will get back to you on that after I ask my father.
5. Until he/she is a few weeks old, the size of the bin doesn't really matter. Just so long as he/she has good bedding (we usually use sawdust), he/she will be comfortable. At about four weeks, he/she will be more interested in exploring. That's when we added some wood planks to the top to keep them from hopping out without completely covering them, and started taking them on short trips outside (always supervised, of course, because we have hawks very near by). Food and water isn't necessary until day three, but it's nice to have earlier. They can live for the first three days without, but we've noticed them start drinking on the first day. Just be sure to add some rocks to the dish so that he/she can't fall in, because if he/she gets too wet, sickness is sure to follow, or if the dish is too deep, climbing out will be much harder than falling in (once they're wet, it'll be harder to hop out). As for the food, they'll enjoy having it to peck at. Once they're a few days old they'll even enjoy spreading it around a bit.
6. Chickens do enjoy having company. If you can't be holding him/her a lot, company will probably be good. Just remember to keep an eye on them. Chickens establish a pecking order, and the youngest is a prime victim to be bullied every time there's a squirmish. Even if they don't mean to, they could accidentally walk all over him/her. Some friends will be nice for him/her, and you can get them as soon as you like (it might be best to wait a few days, though) just make sure everyone is treated fair.
7. Vaccines are always recommended, although we have never given our chickens vaccines. We have three year olds that were never vaccinated and are doing just fine; we do start the hand-raised chicks on a medicated starter mash (although, for future reference, if there's a broody hen hatching any eggs, you can give them regular starter mash; they'll get all the immune system boost they need from pecking at mama's poop!) If there are a lot of chickens in each enclosure, a vaccine might be a good idea. We have six enclosures, each one having no more than three hens and one rooster (yes, we have five roosters; one Americauna/Buff Orpington mix, two Bantams (a slightly smaller breed), and one Serama (a very small breed; he stands no taller than the entire length of my palm)). Our enclosures are all designed around having a small cage-ish area for the night (our biggest chickens have a large dog carrier that we close each night) and a larger are where they can scratch and rummage for insects during the day. Whether or not you get them vaccinated depends on how close they'll be to how many other chickens.