Did Luther think Israel and the Church were two different things? Did he believe in the promises made for Israel as a nation? Was he anti-Semitic when he reformed the church? Did he become one later?
Like most of his contemporaries, Luther understood the Jews to be evil. Anti-semitism was common in that era and was unremarkable. Jews, as spawn of the Devil (and I'm purposely getting into character here, not espousing this!) were creatures to be pitied at best and disposed of when they got in the way.
The title of his book On Jews and Their Lies gives away his attitude on the subject.
To Luther, the fact that God had originally given the law to Jews was interesting, but irrelevant. Jews and Christians clearly came from the same place, but had diverged so long ago as to be irrelevant. Christ-Killer rhetoric was acceptable, and since error has no rights, there was no problem with putting them to death.
At best, Galatians 3:24 would have summarized the relationship:
So then, the law was our guardian until Christ came, in order that we might be justified by faith.
Christ having come, the guardian was no longer necessary, and the people to whom the guardian was first introduce had clearly been forsaken by their maker, so no particular privilege was seen. Jews were infidels and heretics on the level of Mohammedans.
A modern person, of course, would (or at least should!) be completely appalled at such a characterization. Tolerance was not a virtue in Luther's day, for the simple reason, it was unnecessary. You were a Christian if you lived in Christendom. If you weren't, you were inviting God's wrath upon the community, were a degenerate and a rabble rouser, and you threatened the entire order of society and impaired its ability to look after its welfare.
Within that world view, however, Luther was remarkably open to seeing that anti-semitism was not their fault - rather it was the fault of the Catholic Church. He wrote:
If I had been a Jew and had seen such dolts and blockheads govern and teach the Christian faith, I would sooner have become a hog than a Christian. They have dealt with the Jews as if they were dogs rather than human beings; they have done little else than deride them and seize their property. When they baptize them they show them nothing of Christian doctrine or life, but only subject them to popishness and mockery...If the apostles, who also were Jews, had dealt with us Gentiles as we Gentiles deal with the Jews, there would never have been a Christian among the Gentiles
To be fair, however, the American concept of Individuality is much, much more modern and western thing. It is a byproduct of modernization - and to judge Luther for it is anachronistic. It would be akin to judging Galen for supporting the concept of imbalances of the humors as the cause of disease. Knowledge changes over time, and Luther, like his contemporaries, simply had a worldview shaped by the lack of much outside of the Church. In the same way Rome was pagan and the West is modern, Europe in the time of the Reformations was Christendom-focused.
Note: The nation of Israel did not exist as a political entity from 70AD until 1948. Living in the early 1500s as he did, it was a long way in either direction.