Anyone can answer...

How do I get/capture/find/slave/recruit FULL FURRY CHARACTERS? I mean Beastkind characters

Do they ramdomly created at finish a dungeon or do they get in an event on them?

If not, how do I get them?

As far as I can say, they are relatively rare to find. I usually find beastkins only in the stock of the special slave trader.

 For this reason, I normally start as a beastkin and my starting servant is also one.

Currently they are only 'guaranteed' as randomly generated characters, so you'd have to purchase them. More options/markets will be added later.