Artificial tears or allergy drops will not hurt your eye lids. One good way to get the drop into the eye and not waste it by having the drop land on the lids, is to instill the eye drops by looking into a mirror (a magnifying mirror works great). Look directly into the mirror, gently pull the lower eye lid down and place the drop into the lower lid pocket, then close your eyes for a minute and dry your lids.
I dont think so. But if your eyelids itches then there might be some issue. better consult an eye specialist.