I'm not a big proponent of routine prophylactics, I am a big proponent of quarantines. But if this guy is taking care of his animals, there's no harm in asking him what his deworming regimen is. Particularly when you have several species sharing the same space, who can potentially host...
In terms of shelter space, that seems to be plenty. I have a 10x16 (roughly) space for my goats, they have a favorite corning, take up about 1/4 of it. The chickens use the rest. It IS important you have a way for them to sleep up off the ground, and you need a way to provide them goat...