basically you just move your jaw up and down. to get different types of vibrato you change how deep the movements are and how fast you do them. that "wah wah wah" vibrato is probably a deeper vibrato, so you would have to make bigger jaw movements than you might otherwise do.
to fade out just move your jaw slower as you get quiter. and the type of music you're playing dictates if it's okay if the pitch drops. if you're playing classical then it's not okay for the pitch to drop, but jazz is more open-ended. it would be okay for the pitch to drop during vibrato at times. you could even use it as a type of "special effect"