"The water, please!"
Translation:Το νερό, παρακαλώ!
I wish you could hear the pronunciation on these questions. Or at least after to answer it.
I have heard native people use "σε" or maybe "σας" before παρακαλώ & ευχαριστώ.
What do they mean for the words?
You are literally saying "I ask" and "I thank", so to complete the thought, "I ask you" and "I thank you".