1. All Cream Legbar-Barnevelder will produce green eggs. My f1 tends to be spring green (a lovely color). If your CL is pure, she will have 2 blue genes, meaning every progeny will receive 1 blue gene which is dominant. The brown wash is trickier to pass down, and it takes some testing with the rooster to tell how "dominant" his are, so whether you get spring green or olive is depending on that. I was very happy with my F1 CL/Barney eggs.
2. Yes, BR/Barney will be sexlinked with black females, black with white head dot males turning into barred adult males (often with some red bleed through at the shoulders).
3. Your CL/Barnvelder f1 will produce sexlinks as well as the CL girls are single barred while boys are double barred (they are an autosexing breed if bred CL to CL). Unfortunately, in my experience, they are just a bit harder to detect as the single barring gene passed by the female to the boys doesn't always display as well on a lighter chipmunk that I tend to with my CL-Barn crosses (it can be a whisp or a stripe on tan). However anything with a streak of white on the head in my line has been boy. Girls are a solid chipmunk with NO head striping whatsoever. But for safety, let these grow out as you don't want to mistake a girl for a boy if she simply has some color variety.
Happy hatching
LofMc