1. For hand quilting, I love YLI 40/3. It is really very nice. If you're going with Aurifil, I'd pick a 40wt & you'll also need either bee's wax or thread conditioner so you can work with it more easily. I think 12wt or perle cotton will steal attention away from the beautiful applique work. I really wouldn't go heavier than a 28wt.
2. When I quilted my SBS, I did off white in around the applique & roughly matched the color of the outfits when quilting on the applique. If you do go with a color, I would probably stick to something pale -- light grey, pale pink, or a dull pale yellow -- so it complements, rather than competes with the many fabrics in the applique/piecing.
3. If you hand quilt, I'd quilt 1/4" around the applique. For machine quilting, I like quilting in the "ditch" around the applique as it will make the applique puff up a bit.
4. Honestly, I really like the edge with just the crochet; I'd add facing to the top & backing, and set the crocheted lace just inside on top of the batting (maybe consider trimming a bit of the batting away to reduce bulk) and then would stitch it together with a white perle cotton or Aurifloss. I don't think I'd add any additional fabric, but if you do, I'd go with just the yellow for the border & binding to keep the attention on that incredible crochet.
It's always such a tough thing when I have techniques I really want to use, or fabric I really want to incorporate to pull back & think about what I want to be the star of my quilt, but sometimes less really is more. I think by keeping things simpler, the fantastic heirloom vintage quality of your quilt will really show through. In any case, it's an incredible quilt & I can't wait to see what you do with it!!!
