It would be really convenient if in advanced search they added a feature where you could search up a certain colour and all pets with colours in that range would show up. Also a NOT option like for example while searching for pets you could look for a faelora with jingle bell harness but NOT spotted flower so no faeloras with both would show up.

I like the first idea but I don't really get the second one? You can search for a certain gene and put none In others?

For example if you are looking in advanced search for vunlyxes with galaxy stripes but you keep getting vulnyxes with galaxy stripes AND tiger stripes but the tiger stripes keep muddling up the galaxy stripes you would be able to click a button near it which would remove all results with tiger stripes.

Why not just say carry or nothing instead of having a separate button? Unless you are talking about having another gene on there too lol

You can do that exact thing already. Using your example, all you have to do is set 'Gene 1' (the one with tiger stripes) to the selection 'Nothing'. Then when you search it only shows you results that don't have anything in gene slot 1 :)