Any collection of filters and sources can be saved as a segment, and all segments dynamically update as you receive more responses through screeners or upload new CSVs. You can always click the save... button to save a segment, and you'll be presented with some options:
Add to Folder
For now, you have to create a folder before this modal, clicking the three ... next to the segment folder dropdown (see below). After you've created the folder there, come back to this save modal, and you'll see the folder in the list.
Only owner/admins can lock or unlock segments, similar to Rules & Automations. This prevents anyone else on the team from modifying the segment in any way, including filters or sources:
New participants that match that segment will still continue to be added to that segment, so it's not locked from new participants. It's only locked from being modified. You can also still drag a locked segment inside a folder, which will change the order of segments for everyone. Alternatively, the order of segments in "All Segments" is set per team member individually.
Tldr; you have your own order of segments for the top level, but inside folders the order of segments is the same for your whole team.