Before captivity, you would make sacrifices. But during, they couldn't go to the Temple to make sacrifices, so they just obeyed the laws.
Before captivity, they would have a priest to assist in worship. During captivity, they didn't have a priest, because they didn't have the Temple nearby, but they had teachers, or rabbis, who were with them in captivity.
Before captivity, Jews believed that God caused everything to happen, including evil. With the influence of a Persian prophet, they now believed that God was good, and Satan did evil.
Before captivity, Jews were monolatrists: they believed in one tribal god. Their god lived witht hem and was nomadic like them. Now because they were all spread out, their god had to be with all of them. So they became monotheists, believing in one universal god.
Before captivity, they were chosen people. After captivity, they were still chosen, but were also a grand people, because their god had freed them.
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One difficulty in knowing who Jesus was is that he didn't write anything down himself. The gospels were written by his followers, and long after he was dead. Matthew, Mark and Luke all came from the same source, and Mark was the oldest.
Another problem is that the author of Mark was ignorant to some things, never knowing Jesus himself. He made geographical errors: he had Jesus going in one direction to a city when the city was actually in the other direction. We think the author was a Roman because of his pro-Roman attitude. He makes out the Jews to be mean and bad, and the Romans are good. Also, there are mistranslations in the text from Aramic, the language all Jews were fluent in, and Greek. If he was Jewish he would have known Aramic.
Another difficulty was that the stories of Jesus' birth are contradicting to history and each other. The gospels tell us that Jesus was born under the reign of Herod the Great, and during the Roman census. Jesus was (supposedly) born in the year 0. We know for a fact that Herod died in 4 BC, and the Roman census wasn't until 6 AD, so we can't really be sure of his birth date. Also, one gospel tells us that Mary and Joseph went to Bethlehem (to be counted in the census), and another says that they already lived in Bethlehem, and only left when Herod started killing babies (which there is no other account of). Plus, the story of his birth was added to the gospels only to make Jesus seem more miraculous.