Does floor beneath end up wet either from leaking or from birds drinking?

Yes they can if the pressure is too high or the birds "play" with the water. You can figure 10-12 birds per nipple, too many less and they tend to play with the nipple at times. Depending on the bird size but at most you only want 1/2-3/4 of a PSI of water pressure. Your water source, if gravity fed should only be between 12" - 18" above the bottom of the nipple.