I thought that the word please came from the plural of plea. But then why is it please instead of just pleas? Why the e? Are "plea" and "please" really related to each other?
Surprisingly, plea and please are not derived from each other. The verb please comes from Old French, and ultimately from Latin:
please (v.) early 14c., "to be agreeable," from O.Fr. plaisir (Fr. plaire) "to please," from L. placere "to be acceptable, be liked, be approved," related to placare "to soothe, quiet," from PIE root *p(e)lag- "to smooth, make even" (cf. Gk. plax, gen. plakos "level surface," plakoeis "flat;" Lett. plakt "to become flat;" O.N. flaga "layer of earth;" Norw. flag "open sea;" O.E. floh "piece of stone, fragment;" O.H.G. fluoh "cliff").
The word plea also comes from Old French and ultimately from the same Latin word as please, but the stems were already different in O.Fr., and there is not and never has been any morphological relationship to please in English.
plea (n.) early 13c., "lawsuit," from Anglo-Fr. plai (late 12c.), O.Fr. plait "lawsuit, decision, decree" (9c.), from M.L. placitum "lawsuit," in classical L., "opinion, decree," lit. "that which pleases, thing which is agreed upon," properly neut. pp. of placere (see please).
All etymologies from Online Etymological Dictionary.