Why does God send Death to Everyman?
God is unhappy with the way Everyman is living his life. Money is one factor, but there are many others. Remember that Everyman is one of the first morality plays, and it would be performed in church to teach the every day folks who didn't read and write how they were supposed to live. Plays of this type were a common and successful way of teaching the illiterate masses the words and ways of the Bible.
After Death is sent to deliver the message to Everyman, he goes through the typical reactions--denial, refusal, acceptance, and then he seeks company to travel with him. Of course, once everyone else finds out where he is going, they all find something else to do. Only Knowledge and Good Deeds go with Everyman to judgement day and the grave.