You can set it with eye shadow, this may cause sensitivity to the eye though. Otherwise, just try different eyeliners, different formulas may be longer lasting on the waterline than others. I prefer...
You could use MAC Fluidline, which is a gel liner. All liquid liners are not that waterproof, but I don't think that all of them can be applied to the waterline.You could also use MAC eye kohls, but...
Yes, if it is waterproof. If it is a pencil make sure to sharpen it before and after every use in there as it shaves of the layer that touched your eye. If you use a brush be sure to wash after...