Mixology doesn't actually need any fruit to function, an empty bar will still produce drinks. If you're not doing a Dynasty life fruit is always a Sim pleasing addition though. Just don't add plasma fruit, as that will make non vampires ill after drinking.
As far as I know, there is no progress number for mood drinks, but I did manage to finish that challenge myself, and it should complete when you've made enough. It takes fifty platters of mood drinks though, so it's going to take a bit of time.
The challenges aren't easy, but here's a few tips that made it do-able for me 1) Get the fast learner LTH reward, so that they pick up new drinks a little faster. 2) Drinks served from your home bar to other Sims you control still count as "Sims served" as long as you're "tending the bar" at the time. 3) Don't be afraid to "clean up" some of your extra drinks while leveling your skill, it really frees up extra space.
I hope I was able to help, good luck, and happy Simming!