#1
Me and my guitar teacher have gone over "complimenting" the song (correct me if Im not saying it right) in jazz songs, and he said if I get good at the song I can walk which is what I really really want to learn

Im not really sure how to go into it though
#2
I think what you mean is "comping," or accompanying.

Anyway, with the the walking, you basically just put other bass notes in between the root notes of the chords.

Like, if you have a chord progression like Cmaj7 - Amin7 - Dmin7 - G7, you could play a bass line like

C (G#) - A (C#) - D (Ab) - G (B) then back to C, or something along those lines.