You can use the same sheet music. With practice you'll learn the idiosyncrasies and character differences. There are quite a few YouTube videos, some from bluegrass greats. There are also videos of guitar players playing the mandolin like a guitar.

Starting off, master alternate picking(up-down-up-down) as it gives you the most speed. There's cross picking but that's not something a beginner needs.

Get a collection of picks together of varying thicknesses and materials. They're cheap so might as well get a variety.

Tremolo is a skill that will be most important skill needed in that style. Tremolo is rapid picking of a note in succession. You may find one pick type may work better for it than others. In bluegrass styles you'll want to eschew open chords and learn to chop them rhytmically.

If you can already read sheet, you're already ahead. Though mandolin is mostly a folk instrument, vivaldi has composed music for it.

If you're mostly focused on violin, the mandolin can make a good secondary instrument to it and I don't see the need to get formal with it unless your heart is set on it(for example, Sam Bush was a fiddler but he's most known for his mandolin playing).

For me, the mandolin is just there when I'm in the mood to pick because sometimes you're just in a picking mood. It's not my main instrument.