There's likely to be some incidental music from John Williams to retain continuity with the older series but most of the music is by the Swedish composer, Ludwig Gorannson, who is following in John Williams footsteps, as far as the music goes.
Yes, there is!
Watch the scenes featuring the two New Republic pilots: first in Chapter 9, when the two rescue Mando from ice spiders, then in Chapter 12, when Carson Teva gives Cara Dune with his medal. In both scenes, the score is a slowed-down, melodramatic cover of John Williams' 'March of the Resistance' from the sequel trilogy.
Here it is on the ...