Licking their eyes is normal--since they don't have eyelids and can't close their eyes that is how they keep them moist.

They lose their tails in various ways--rough handling, a bite from or scuffle with a cagemate, in response to some sort of fear or trauma, during copulation, etc. It is quite common for them to lose their tails and sometimes entirely unavoidable. You might have a crested that you've owned for several years and one day you walk in and its tail is gone--it's just one of those things.