1. Yes, he is.
2. The Scarlet Witch used magic to become pregnant, and Vision is the father because he was holding her when she did the spell. Or something. It's magic, we don't have to explain it.
3. No, he and Billy are not only not biologically related to Wanda and Vision, they're not even biologically related to each other - they were born to different parents.
The comics are unclear on exactly why and how they were reincarnated, or how they can be teenagers if their souls were reincarnated when they were babies. But, you know, "Marvel Time" and "it's magic" can explain a lot of that.