Why is "Thou shall not kill", repeated to the Jewish people again even after it is given to Noach? Does this give religious Jews a higher level of ethics? If so, how can we serve in the army with non-religious Jews today, and how did the original Zionist rabbis (like Rav Kook) justify building a joint state/armed military alongside them?

Yes, it means that Jews have a different level of ethics, but sometimes the Noachide laws demand even more, e.g. they are forbidden even more severely than Jews for aborting fetuses. But this has nothing to do with the continuation of your question which doesn't deal with Noachides but with secular Jews. Obviously religious Jews have a higher level of moral demands than non-religious Jews, but that doesn't prevent us from working together as brothers in Am Yisrael, but rather obligates us more! This cooperation and mutual love and respect for all Jews is part of the mitzva of Ahavat Yisrael, and also enables and obligates us to hopefully raise them to that higher level. Remember, the redemption is not just for religious Jews, but for all Am Yisrael (e.g. only 7% of the Jews in America are religious), who are all "sons of God" and part of the Chosen People. Judaism is not just a religion but also our nationality, and accordingly, all agree that even the non-religious are just as Jewish as the religious. Regarding the question of serving in the army with them, we are obligated to protect and save all Jews, as are they, and that's why it's davka beautiful and commendable that we serve together in the IDF, which greatly solidifies our national unity (Achdut) and mutual respect. One of the leading (formerly) anti-Zionist rabbis, Rav Yissachar Teichtel, was also greatly bothered by your question, regarding working with the non-religious Zionists. Only after the Nazi invasion, when he had to go into hiding, he had time and was forced to think about the issue in depth, and wrote a 300 page book, "Em HaBanim Smeicha" (also translated into English) changing his direction, and writing how the Talmudic sources actually obligate (!) to join with the secular Zionists to build the Holy Land. I highly recommend it for you, if these questions preoccupy you.