I never knew Alex (drums) was Eddie's brother
Yeah, Alex originally played guitar too, and Eddie played the drums, crazy! 
to produce 12 studio albums with 56 singles, you have to be pretty talented
That is a lot, I like Jump, that is my favorite song. 
Push Comes to Shove is one of my favorites. Have you seen them in concert?
Yes, I can play Push Comes to Shove on guitar, the solo is very good. Has some cool tapping in it. 
Do you learn their songs from a song book or just by ear?
By ear mostly, I've been playing a long time. Van Halen is tricky though because he uses a lot of wide stretches. 
He is ranked #8 on Rolling Stone's greatest guitarist of all time. He's also quite a guitar collector. do you collect guitars?
I have 5 guitars, Fender strat, les pauls, and a wolfgang EVH guitar.