With my limited understanding there are some possibilities I can tell you. First I want to break down the feather types, I know you did specifically ask about colour this is just in case you didn't know. Your frizzles carry 1 gene for frizzle as it's a (co-)dominant gene, if it's 2 genes I think it's called a frazzle and they have health problems. When bred with a non-frizzled bird 50% of their offspring will be frizzles. The naked neck is also a dominant gene. Recently in another thread I read that heterozygous for this causes the breast/crop area to still have a patch of feathers, while with homozygous it's also bare skin. If they are homozygous all their offspring should be showgirls as well.
Cuckoo is a dominant gene so it can be expected that all your chicks will carry 1 gene for this and show the cuckoo pattern. I do not know how it would show on mottled birds, so I can't say anything about that. But cuckoo can combine with partridge, Bielefelders show this combination often. The cuckoo pattern genes causes white stripes to appear. This means that the normal chicken colour is whatever colour the other stripes are. If your rooster has black stripes this means that he carries black. I know buff coloured cuckoo patterned chickens exist and you can google this for pictures. But for as far as I know black is dominant to buff. So the offspring should still be normal cuckoo colour and pattern, while still carrying the gene for buff colouring.
Finally cuckoo is sexlinked, so the chicks can immediately be sexed at birth. I vaguely remember reading somewhere that fibromelanosis doesn't mix well with the cuckoo pattern, but I don't know how that works.
