No I don't think Snape would have joined Voldemort. I think perhaps the only reason he got into the Dark Arts at school was for power. I mean, people had walked all over him his whole life, so it's understandable. Having Lily would not only make him happier, but soothe his ego.

I think he would've still been reserved, but not malicious.

It's very hard for me to imagine Snape with a child. I think he would've been strict because he values self-discipline. He would make sure they kept their grades up. I don't think he'd be the open father in the world, but he would definitely love his kid.

Definitely think he would've taken more care of his appearance. I agree with The Cursed Erkling about using his appearance to distance himself from others.

As for singing and dancing...no. I just can't see that. Maybe humming. Humming would work.