Remember, the Mosaic law (comprised of 613 commandments) was designed to structure life. The commandments cover every aspect of life and range from compensation for damanging another’s property, to food preparation to sexual activity within marriage. There was a daily rhythm to expectations… as well as seasonal. For example, there were three festivals were an observant male was required to go to the Temple (Sukkot or the Harvest festival, Pessach or passover and Shavuot which is the anniversary of the giving of the law and is 7 weeks after Passover).
Modern traditional Jewish observance flows around the calendar (the six days of the work week vs Shabat, and the holidays (Starting with Rosh Hashana, Yom Kippur, Sukkot, Simchat Torah, Chanukkah, Tu Bishvat, Purim, Passover, Shavuot and Tisha B’av)
It is accepted practice to believe a person if they claim to be descended from a specific tribe. In particular, the Cohanim (the priests or descendents of Aaron) and the Levites require a positive knowledge of family descent. In traditional Judaism, a Cohen (priest) is allowed (after age 13) to give out the priestly blessing in public during certain holidays. Also, a priest and levite will be given precedence for honors (being called for an alyiah or to introduce certain prayers like grace after eating). There are several prohibitions on priests besides not touching a corpse: for example they cannot marry a divorced woman or a convert.
The term Rabbi (technically translated as “my greater”) is a recognition of having attained a certain level of knowledge in Jewish Law. A Rabbi is not required for prayer… or technically for a Jewish Marriage (the husband technically marries the wife and that is witnessed by two adult male Jews in good standing) or any other ceremony.
There is ONE ceremony where a Cohen (priest) is required: the pidyon HaBen (or redemption of the first born if Male).