Moe is presumably a countryside local just like his customers and acquaintances. He may have been one of Posey's victims when she was roaming around.
Moe thinks well of Duane and will treat people sent by him properly.
There is nothing known about what Moe looks like.
Moe is either in the back of or away from his Hamburger Hippo stand for the entire vampire trial Darkwing Duck is put through, which makes Duane's advice to tell Moe he sent him and Launchpad useless.