#1
As I had go to a classical guitar teacher, I didn't learn the correct vibrato technique (also had a lot problem with pick holding and bending, both are good now). Where can I find some good videos or articles about it? It helped me a lot to keep my thumb over the neck instead of keeping it at its back, but still it doesn't sound really good.
#3
Classical vibrato isn't wrong. It's just different.

I, myself don't have vibrato and bends on the electric down yet, but getting there. Something that helped is something I've read repeatedly on this site: switch to the "baseball bat" style of holding the guitar and use your wrist as if you were turning a key.