There are a number of pieces of advice I would give someone in your situation, Gamera, speaking as someone who came to the Catholic Faith through studying (Orthodox/Hasidic) Judaism.
First and foremost you have to know the particular Jewish tradition that the people you are speaking to hail from. A Reform Jew is going to have a different perspective from a Conservative, and both groups will have significant differences with typical Orthodox Judaism, and even within Orthodox Judaism you will find a big difference in perspective between Modern Orthodox and Hasidic Jews. Unless you have a good foundation for understanding the particular path of Judaism you are engaging, you will be immediately lost in the dialogue.
Which brings me to the second bit of advice: dialogue, don’t debate. If you approached the discussion in the same manner that you might approach a “Scripture-proofing” debate with a Fundamentalist Protestant Christion, then you’re not going to get anywhere. As Kaninchen pointed out, you’re dealing with a fundamentally different paradigm of belief. Questions like “who is saved?” just don’t compute in any path of Judaism. A better approach would be to focus on humanity’s relationship with God in general, and what our response should be to God’s self-revelation.
Thirdly, while it’s certainly true that there is a fundamental paradigm difference between Judaism and Christianity, it is important to remember the reason for this paradigm difference is the coming of Messiah itself. In Judaism, particularily Orthodox and Hasidic Judaism, there is supposed to be a paradigm difference between pre- and post-Messianic Judaism. Apostolic Christianity (Catholic and Orthodox Christianity, specifically) are historically rooted in this necessary paradigm shift; the Jews who founded the Church were openly dealing with the reality of the changes in Judaism that come with the revelation and coming of the Messiah. It’s a mistake to assume that modern Jews of any stripe will recognize Christianity as “Judaism + Jesus”, since there is no clear concensus, even among Messianic-oriented Jews, of what “Judaism + Messiah” will actually be like, and how it will engage the world of Gentiles. Remember, this was a HUGE issue even within the first days of Christianity, with the Book of Acts and many of the Epistles wrestling with this very question of perspectives. One only has to look at the debate over Judaizing within the New Testament to see that it took a lot of soul-searching and debate (and, I would say, the Inspiration of God) to settle the question of how to approach the world in light of the revelation of the Messiah.
When you engage Judaism you are coming from a tradition that has settled this paradigmatic question thousands of years ago (speaking again of Apostolic Christian Tradition) and moved on to other issues, and certain things that seem “crystal clear” to you are based on this fact will not be clear at all to any Jews you speak to, regardless of their particular tradition of Judaism. Some things only become “clear” precisely because of the coming of the Messiah, and there’s really no way of arguing about them with modern Judaism because there is a whole aspect of Judaism that “hasn’t happened yet” according to their beliefs (well, most of their beliefs, there are some Hasidic Jews who DO believe the Messiah has already come, but that’s a whole other issue).
On top of all that, Judaism hasn’t been at a stand-still since the time of Jesus, and there have been many developments and approaches that have occured over time, some of them even in response to Christianity. Simply regarding modern Judaism as “Christianity without Christ” misses the fact that even in the time of Jesus Judaism was not a singular entity; we see in the Gospels, for example, that there were huge differences between the Sadducees, the Pharisees, the Zealots, and the “Baptizers” (referring to John the Baptist’s group, which may or may not have been Essenes). Judaism, since that time, has witnessed the elimination of the Temple, the disappearance of the Sadducees and Essenes, the rise of Reform Judaism, Zionism, and Hasidism, and countless other important things. To miss out on these developments is to basically completely misunderstand who you’re talking to; one only has to look at the debates between Jews and Christians two thousand years ago versus the debates today to see that expectations and world-views have indeed shifted.
As for the particular points you raised, I won’t address them now because I don’t know what tradition of Judaism the person was coming from. I also don’t know how valuable it would be to argue some of the points. Hope this helps somewhat!
Peace and God bless!