As religious Jews we believe that the Torah is a complete covenant with the Jewish people. There can never be a 'New' covenant as the Torah clearly says that the covenant with the descendants of Abraham, Isaac, and Jacob is an unbreakable decree. Even when the Jewish people have gone far from Torah, Hashem says that he will be a patient father and await our return. We do not need any kind of 'saving' from any non-Jewish sources, as the Torah clearly sets out the method of rectifying our sins. The primary way we can rectify our sins is through the Temple service, but the Prophets knew we would live in exile for many years without the Temple, and the Torah also provides other ways a man or woman can repent of his/her sins.
The Moshiach is not necessary for a Jew to do his/her commandments. The Moshiach is not a magical or supernatural entity (as it seems he was made into in other religions). Moshiach will be a man of skin and blood, he will be born of a father and mother, he will have a lineage through his father going back to the Davidic dynasty. All of these things are clearly explained by the Jewish prophets.
When Moshiach does come he will gather the Jewish people from the exile, he will go to war against those nations who despise the Jewish people, destroying them utterly. At this time the messianic age will be upon the world and the knowledge of Hashem will fill the world like the oceans.
A Jew must reject dualism or polytheism (trinity) as it goes against many of the statements Hashem made to the Jewish people. The unity of Hashem is one of the most basic principles of Judaism and is one of the main reasons Jews will reject any other belief system.