Lets answer your question(s) one at a time.
How many souls can I carry in it?
Just one at the time?
I guess when I'll be using it to perform enchants, it won't disappear
but just become empty, right?
The Black Star has two states: Empty and Filled with [inset soul level here]. Since I tend to have a bunch of petty through greater soul gems on me at all times I don't have to worry about storing deer or elk souls in my Black Star (what a waste that would be). In Skyrim souls will be stored in the lowest leveled compatable empty soul gem in your inventory confirmed here.
If an empty Soul Gem is available in your inventory, then the soul will fit into the smallest Gem available...
For more information about soul gems, the black star, enchanting and soul trapping see this link. At the bottom of the linked page, under "See also", you will find the additional links.