In regards to some of your issues
#1- I discovered this quite by accident but if you go to the "My Account" page there is a box you can check that will allow the gender of all boxes in both the cattery and pedigree to show.
#2- I'm afraid I don't quite understand what you mean by being able to see the visible and the dominant. I see the same information for boxes listed in the same way as the pedigree (except for the creation date)
#3- This could be helpful to change, but since I keep all my boxes in the cattery I can't see it making much difference for me
The issues concerning passing cats to alts and not being able to follow their trees or not being able to follow the tree of cats you previously owned is aggravating. However, as mentioned, some people are very particular about privacy matters and have voiced their opinion in opposition of being able to follow trees up through cats you don't own(whether you gave them to an alt, sold them, whatever). I don't quite understand the part about following a cat from box to parents but not parents to box. If I want to see what sort of offspring a cat has produced I simply go to that cat's pedigree and the offspring are shown below, including the ones I have sold although I can't click on them. I haven't used my alt's cattery/pedigree enough to have encountered this problem if it is related to passing cats between alts.
#6- Thus far I haven't encountered this problem.
Although that was mostly rambling at least, hopefully, there's at least a solution to the first problem in there