They look to be fowl pox, it will usually run it's course in a few weeks, it's transmitted by mosquitoes, there's a lot of it this year, there's no treatment, make sure they can eat and drink fine, if they start looking under the weather put some antibiotics in their water, won't help the pox any but can help if something else gets them, otherwise not much you can do. It's hit and miss as far as spreading, nothing you can do for that either.
No, please don't do that, they should be fine, it can take up to six weeks from the start until they are all gone, it looks like you are a couple of weeks into it already.
Sounds like it's in the mouth as well, that would be wet pox, that I haven't dealt with but know that's a lot worse, I would do a search on this site, there a plenty of old threads that talk about it.
Vaccines can help those that aren't infected avoid getting it. I personally didn't vaccinate because I believe in building a healthy immune system and culling those who can't. I would put your young chicks on antibiotics just to help their immune system along, I wouldn't mess with the sores too much, I believe the scabs can be infectious, so try to minimize handling especially if you also have other poultry to care for.
It does take a while to completely run through and heal, and some of my turkeys eyes swelled shut and I didn't think they had eyes anymore. You could cull, but I would only if they were suffering, otherwise it is already in your environment and getting rid of the chicks I don't think would help you. Good luck.
Where are you raising the chicks--inside or outside? It looks like pox, but ant bites can also look very much similar. Do you have mosquitoes out right now, or have you noticed ants, or any pecking of the eyes? Fowl pox, if that is what it is, is a virus that usually takes 2-3 weeks to go away. Eye infections can be common, so something like Vetericyn eye gel or Terramycin ointment would be good to use twice a day in the eyes. Sorry for the loss of your chick, and I would make sure the chicks are eating a drinking. If you see any yellow material inside the mouth, that would probably be wet pox, which is much more serious.
Sorry for your loss. It seems that fowl pox must be more harsh on young chicks. I wouldn't be surprised if the chick doesn't lose sight in her eye if she recovers. I would try to dig out any pus or solid material in the eye, flush with saline, and apply some Terramycin or Vetericyn eye gel to the eyes twice daily. If she recovers, it will be sad that she will be an only chick in her age group. Have a look at these pictures and captions about pox: http://www.thepoultrysite.com/publications/6/diseases-of-poultry/195/fowl-pox/