Hello... for the module questions...
1) We have an upcoming events module that will list events, but not one that lists only events that the logged in user has registered for.
2) Also not available to have a list that auto-populates based on the the logged in user's location.
JomSocial questions...
1) Group events in JomSocial are not supported yet. We will be working more in that direction over the coming months.
2) Frontend event management has been available since the launch of DT Reg 2.7 in Nov. 2010. You can setup permissions for what users / user groups have permission to do certain functions for creating events, categories, locations, etc.
3) JEvents is no longer required, but still an option to sync with. DT Register adds registration functionality to a JEvents event when you use the sync option. This requires first creating the event in JEvents, but then it has to be setup separately through DT Register to add the main functionality.
4) Possibly, nothing in the works right now, but possibly later. Next step will be a plugin that will show "My Events" inside of JomSocial so the user can list their own managed events that they've created in DT Register and provide access to them from their profile. That is coming.
Thanks