If he had a freckles on his underside (and no, um, male parts) he would look just like my female Gossip. She sits with her head curled like that and sleeps just like that !
No idea, sometimes with mixes it's so hard to tell what the parentage is. I do think that your dog's head is a bit more refined than many of the pit mixes i've seen.
I agree with the others that although he seems to have Basenji in him - his head is def. not Basenji.
As for the leg I'd have it amputated if it troubles him - He'll cope with 3 legs I'm sure, but certainly consult a specialist first. Please keep us updated.