Answers...
1. I wish there were shortcuts, but unfortunately not. However, there is a slide bar that appears on the far right side that will allow you to zip right through the alphabet very quickly. I watch the first letters on the left while using the slide bar. I can easily stop at any letter without much effort.
2. When browsing through your library, there are 3 vertical dots on the far right side of the artist, album, and tracks where tapping them brings up a menu allowing shuffle play.
3. Not that I know of.