(1) Kindly remember that many years ago, those words were probably spelled as
two words: any one, some one, every body, every one. Thus you should use a singular
verb, even though the idea of those words is plural.
(2) Do you know anyone who speaks Russian? (question)
No, I don't know anyone who speaks Russian. (negative)
(3) Do you know someone who speaks Russian? (a question when you think the person with whom you are speaking probably does know a Russian-speaking person.)
(4) Someone/somebody called on the telephone for you. I told her that you were not here and to call back in an hour. (an affirmative sentence. That is, it is not a question and not a negative sentence.)
(5) Does someone/somebody have a birthday tomorrow? (question when you are thinking of a particular person and you know the answer is probably YES.)
(6) Everybody/everyone needs to eat and sleep. (affirmative sentence)
(7) Does everybody/everyone at your job have a car? (question. P.S. "have" --
not "has" -- because it follows the auxiliary "does."
(8) Tom: Everyone/everybody likes me.
Mona: Not everyone/everybody likes you.
Tom: Who doesn't like me?
Mona: I don't!
Tom: Why didn't anybody tell me how you felt about me?
Mona: Because nobody/no one knew how I felt.