What is the easiest way to get the newest version of Dwarf Fortress, without losing my current worlds and progress? Is this possible? I don't want to lose my current worlds.
You can't generally play your existing worlds with newer versions. New versions seem to regularly introduce 'breaking changes'.
Typically, players create a backup copy of their worlds before upgrading. I'd suggest either creating a backup copy of the Dwarf Fortress game files too or just keeping different versions in separate locations on your computer. That way you can continue to play existing worlds in the version you know works (assuming there are no bugs in that version anyways) if a world is incompatible with a newer version.