I met an Orthodox Jew and we talked about God. He said it is possible to keep the 613 commandments (mitzvot) and that he was following them. Is this the prevalent view of Orthodox Rabbinical Judaism?
Yes, the view you heard from the Orthodox Jewish man you were sitting with is the modern day Orthodox Jewish view; it is possible for the Jews to keep all of the commandments. I should point out that, by means of rabbinic tradition, they have ultimately interpreted these commands in such a way that although they are in reality breaking them, they have convinced themselves they are keeping them. For example, they are commanded to offer up a day of atonement sacrifice. But they are not obeying that commandment today. The Rabbis teach that fasting is equal to offering up a sacrifice. The logic is: the fat and the blood of the animal belong to God alone and by fasting you reduce the fat in your blood. Therefore, you are fulfilling that command. Yes, they do teach it is possible to keep all the commandments but you have to understand that they interpret them in such a way so they can claim to have kept a commandment while in reality they were breaking it.