Display custom categories from custom content types.

I’ve been looking extensively for documentation about this and can’t find a thing.

I need to do three things:

a. Display a list of all custom categories for a custom content type in its archive page.

b. Display the appropriate custom category for a custom content type in the single page.

c. Add the custom category as a css div class to each posts mark-up.

Any help would be greatly, greatly appreciated! Thanks in advance!!