Thought about salvation

How are the people of Israel (the Jews) saved? Do they have to accept Christ as Lord and Savior as does a gentile? (This according to the teaching of the Scriptures.) Or do they have to accept Christ as their Messiah? Is there even a difference?

Is the old covenant totally gone? Is it simply fulfilled and absorbed by the new covenant? What does the book of Romans have to say? It seems to me that the old covenant has not entirely passed away, been fulfilled or whatever because the Jews are still God's chosen people. That has not changed, has it?

I definitely do not believe in replacement theology or its derivative doctrine of progressive dispensationalism (which apparently places me at odds with DTS and Moody . . . ).