1) Actually, I don't think it's as simple as saying that Jews were cut off to allow Gentiles in to the Covenant. It's not as if God had a seating problem and the only way He could fix it was to kick some people out. The idea is that God ordained rejection for a season that the Gospel might go out to the Gentiles. We were actually blessed by the fact that they did not believe and, you will recall, it was the persecution of the Church that sort of caused the dispersion and the Gospel to be established. But then, Paul reveals, the Jew's rejection is not final but our being brought in is to cause them to be envious of our position and desire to return. I know this is terribly simplistic and I could support it better with Scripture but I don't have much time. The bottom line is that God's purpose is served in saving "all Israel" by grafting us in as a result of some being cut out for a season that they might be provoked to jealousy and be grafted back in. For some, the rejection is not final and Paul is guarding against both that conclusion and a certain twisted pride that some Gentiles might have (like this is all about "us" now and who cares about *them*).
2) Depends on the NT Jew. Paul certainly understood what he was talking about.
A rebel? Of course not, they didn't believe the report.
3) Yes, I think Hebrews really unpacks this in an excellent way in Hebrews 3-6. Read it and remind yourself that the Jews receiving the letter are receiving an argument on the basis of the OT Scriptures.