The first thing to know about pygmy goats is that they are very sensitive. You should never hit or punish them in any way. The only place that will lead you is in the whole. You and your goat will become enemy's.
You should feed your goat at least twice a day. If you have a busy schedule you can feed them once a day, but feed them twice as much as you would if you fed them twice a day. They can belch it back up and chew on it if they need a snack.
There are many illnesses. I will do some research and write down most of them.
There are many clubs that will registrate your goats. The main one people trust is the NPGA. You can print off a page and send to the address they give you. Here is their site, www.npga-pygmy.com.