2681
You could make 14 small milkshakes
2^35-1=34359738367 (over 34 billion - if you made one a second, it would take about 1090 years to do them all!) This is assuming you only make flavor combinations with equal portions of each used flavor, and that you can use up to all 35 flavors, and not counting "no flavor" as an option. If you allow for varying portions, there is no practical limit to how many different flavors you could make, although many would be indistinguishable to humans.
Most flavor comes from the juices which can have a range of flavor depending on many factors. The skin can offer a slightly salty flavor at best, you don't want to know the worst. All in all though I've had flavor combinations that were enjoyable.
Two make combinations you would take 2x1=2 combinations only
9
You could make 10*10*10*26*26*26 combinations, or 17576000 combinations.
Assuming you are using the standard English alphabet, the number of combinations you can make are: 26 x 26 = 676 combinations.
23
8x7x6x5x4x3x2x1
720
20