Interesting insights, Rami!
I am particularly taken with the rabbinic insistence that fasting be tied to providing food for the poor. Quite a number of Christians now make the same connection. For example, a number of Christians of my acquaintance fast on Fridays throughout Lent and donate the money they would have spent on food to help feed the hungry.
Such practices make sense to me. At the very least, they actually feed someone who needs food. They also help the one fasting to remember all spiritual practices have something more than personal benefit or even transformation in view. In the end, spiritual disciplines must not only strengthen our bond with God but also with our "neighbor."
I like your question: "...who are the hypocrites?" Traditional Christian interpretation often assumes Jesus meant some of the Pharisees. Personally, though, I think both of us may be tempted to make a mistake when we ask the question--the mistake of assuming that first century documents ever tell the whole story. My guess is that Jesus had in mind people he knew or encountered, people whose personal practice departed from the norm of first century Jewish life with regard to fasting.
I don't know that I would say fasting's primary purpose is help one "get right with God." Fasting, like any spiritual disciple, may clear or refocus one's mind, freeing it from many distractions, so that it may better apprehend the truth about one's self and the presence of God. As I've noted, this should always lead the individual to better align with the purposes of God, not the least of which is to minister to others. Like any spiritual discipline, fasting is not an end in itself, but a means toward an desirable end.