OK, some more testing maybe points to the problem.
I have a Move Feature in the timeline being applied to a Component. The distance for the move is specified by a User Parameter.
I later decided that I wanted a slightly shorter distance for the Move, so I brought up the Change Parameters dialog, located the pertinent User Parameter and changed it to be half of the previously specified value (went from .05 to 0.25 inches). Now, NORMALLY when I change something in the Change Parameters dialog (and hit tab to bring it to the next parameter in the dialog) the design updates in the window in order to reflect the new value (very handy, glad that it does that). But NOT this time. Nothing changed in the displayed design. When I subsequently got out of the Change Parameters dialog I couldn't do anything, as described in my original posting, above. Fusion just wouldn't let me do anything.
So I quit out of Fusion, restarted my computer, restarted Fusion, and again brought up the same design. Clicking around I could see that I can again use Fusion, no problems like those mentioned in my original post, above. In particular I WAS able to right click on items in the Timeline and the appropriate dialog came up, each including an Edit option. So I went to the same Move Feature in the timeline, right clicked on it, and selected to Edit the Move Feature. But no Move Feature dialog popped up. Instead, Fusion 360 locked up again.
Another Windows restart, another starting up Fusion, another opening the same design. This time I went to that same Move Feature in the timeline and chose to DELETE it. It deleted as expected. But it reported errors. In particular, a bunch of Extrude operations EARLIER IN THE TIMELINE were now red, indicating problems with those Extrudes. But HOW can the deletion of a Feature LATER in the timeline have any impact on Features that are EARLIER than the deleted Feature? This is just baffling. And, as before, deleting that Move Feature cause Fusion to lock up.
I can't attach the Design because of its size.