Question: is there a blue or lavender Cochin??? And how would you come up with the color?
Yes, there are blue and lavender. Blues are part of the blue/black/splash pool. There are multiple ways to achieve blue. This chart might help.
Lavender is totally different. Lavenders must have 2 copies of the lavender gene to look lavender. They can carry one copy and still pass it on to offspring, but they will look visually black - that's called a split. Mating a split back to another lavender can produce lavenders, or more splits.
Another question: if you breed a barred Cochin with a black what will the chicks be? Black?
Barring is a sex-link gene, so it depends which parent is barred. There is also double-barred or single-barred in males, females are either barred or not.
Double barred male X barred female - offspring are double barred males, and barred females
Single barred male X barred female - 25% double barred males, 25% single barred males, 25% barred females, 25% solid females
Double barred male X solid female - Single barred males, barred females
Single barred male X solid female - 25% single barred males, 25% barred females, 50% solid
Solid male x barred female - All males single barred; All females are solid. Males will show a white patch on their heads when they hatch.