I can answer much of this with an image.
In all seriousness, we don't sacrifice korbanos (קרבנות) anymore because we lost the place where we would do it. The Torah forbids sacrificing animals anywhere else, so we had to figure out a replacement. The rabbis of the time decided to formalize prayer to replace the sacrifices, and they created the basis of prayer that Jews have today. More was added as the centuries passed due to stuff happening (the rise of the Christians, the rise of pogroms, etc.)
Also, the different 'flavours' of Judaism (there isn't a good term) do have different ideas.
Orthodox Judaism is the most traditional approach. It holds that Torah and Halacha (Jewish Law) are binding laws from God, and they do not change based on modern trends. In practice, that means keeping Shabbos (the sabbath) strictly, kosher laws in full detail, daily prayer, and traditional gender roles in many communities. They're currently figuring out the LGBTQ community and how they fit in with Jewish Law.
Conservative Judaism values halacha and tradition, but believes Jewish law can develop over time in response to real-world changes. It's more flexible than Orthodox Judaism in that they are more lenient with the laws of Shabbos, they sometimes have mixed seating in synagogue, and will sometimes have female rabbis. They're pretty accepting of the LGBTQ community.
Reform Judaism is the most flexible. It sees Jewish law as important but not binding in the same way. The focus is more on ethics, personal meaning, and individual choice. Kosher and Shabbos observance are usually not kept, and services are shorter and often in English and adapted to modern culture. They are highly accepting of the LGBTQ community.
Basically:
Orthodox = “Jewish Law is binding and central.”
Conservative = “Jewish Law matters, but can evolve.”
Reform = “The Torah matters, but personal choice is key.”
There has always been an orthodox backbone as the jews have moved across the world. As best I can track the main backbone:
We went from Judea to Galilee to Babylon to Persia and the wider Islamic world (including North Africa and the Middle East) to Spain and France to Germany and Eastern Europe and to the Ottoman Empire and Sephardic centres to modern Israel and the United States and Canada and a bunch more communities.
Keep in mind that it split and part of Jewry became what are known as Sephardis (Mediterranean and Spanish), part became Ashkenazis (Eastern European), and part became Mizrachi (Middle Eastern).
Orthodox Judaism dates back to the times before the Second Temple. I've actually thought about seeing if I could track my Rabbi's teachers all the way back (i probably could)
Any more questions? I'll answer them tomorrow. I have to sleep now.