The cup to unlock after the special cup is the leaf cup. To unlock it you have to beat the shell and banana cups in 3rd place or higher, then you'll get the leaf cup.
Yes, of course. It has the same ratio, which is all that matters. You can double, half, triple, etc. any recipe, and will just end up with more or less...
You can unlock the special cup by doing the mushroom and flower cups, and then the star cup. It will unlock the special cup for you when you are finished.