As far as the batting goes, you wouldn't need to add quilting to the sashing. I personally usually like to SID and then add a little design within the sashing just to tie it in with the rest of the quilt. For yours, I'd probably do a narrow little leafy vine running along the sashing & would use the ditches to travel stitch (which is partly why SID is so important -- so you don't have the odd little line of stitching running from one design to the next that's just floating out there without any connection to anything else). It would tie together the print of your fabric & the sections, while incorporating a design that has both straight & curvy elements to it. Leafy vines are a good design for those who are newer to FMQ. It was the first thing I learned after the curvy meander.
Because it's a solid (or near solid) fabric that is carried throughout your entire quilt, it will natural draw the eye to that fabric so my thought is: why not give the viewer something pretty to look at in that section? But it's certainly not necessary. It's entirely an artistic decision.
Nicely done with the FMQ, by the way!!!