Can we remove sync-only device group? Is there impact of procedure?

I highly suggest you to raise a support ticket.

First thing I noticed, which I would focus on first, is that the device trust group isn't in sync. This is the most likely cause of you seeing the "Awaiting IS" in status bar and needs to be fixed. 

Next, the device menu should only display groups your unit is part of, it's strange to me that you can see the status of DR group without being part of it. Was this unit originally part of it, and then moved to DC group? I would think about removing it, from local unit only (and possibly peer?), after performing careful analysis and only if 100% sure that it's now a local object that's not required on this specific unit anymore. 

The sync only group worries me the least. It's in auto sync, which I would change to auto to have more "control" while you fix the groups thing, then sync it manually and move it back to auto. 

But again, you really want to discuss this with support and possibly agree on a step by step plan.