I understand you may mean you want this all to be in the vanilla game, but I'd like to add:
Suggestion #1 is available as mods. The names of the mods should be Bovine Species and Rabbit Species. There's also so many more species that can be downloaded through the mod browser, a lot of which are from the very talented AveryAce.
Suggestion #2 is available in mod form as well! The original mod is a bit overpowered (felines dodge damn near every attack), but the updated and added apon Race & Heat mod adds race bonuses and extra bonuses during the (vanilla) species' heats.
If you do not know where to access the mod browser, click the "enable molded startup" (I think that's what it's called, it's easy to find anyway) at the top of the options menu in the main screen.