I've read a few things about dancer's ugly feet due to dancing; is that only after they have gone en pointe?
Pointe shoes, combined with unlucky heritage, can lead to bunions (look it up for a description). So can any kind of shoe, for that matter. I have very wide feet, and mild bunions from the shoes I wore as a child. My father has more pronounced bunions, his shoes didn't fit as well.
Pointe shoes also lead to callouses. Those are actually beneficial for dance, but look ugly. Bunions are permanent, callouses will (eventually) go away if you stop dancing.
Most immediately, wearing pointe shoes squeezes the blood out of your feet somewhat. Feet look a bit squeezed and wrinkled when they are removed.
What pace should a dancer who just began pointe work take (how long every day, at the barre or in the center, ect.)?
Why not go to a ballet academy and see what their program is for students en pointe? Or look it up in the Vaganova or RAD syllabus.
What is the proper name for a pointe shoe
What sort of exercises should you start with when you're still a beginner?
Again, I would get a copy of the Vaganova or RAD syllabus, Both have all the exercises described. http://www.rad.org.uk/index2.htm