1. No, the effect is randomized (technically). It's not the single serving of latte itself that is causing that specific animal feature, but the overall effect of drinking any latte. If you wish your character to only have 1 type of animal feature though, you're free to have them drink any number of lattes but only get that animal feature. No need to drink old cold nasty coffee!

2. They would not! You have to wait until your current animal parts fade to get a new set, unless you drink a different drink with a different effect which will nullify the first drink and confer the effect of the second for an hour, or until they have a different drink again. ICly, however, characters don't know this.