There is a Date column, it´s probably hidden in your case. Have a look in the RM manual.
After it shows you can of course sort the Rigs by Date.
True, and I always sort rigs by date; however, the OP's second point still applies. If you do a save as while sorted by date, the new rig still goes to the bottom of the list in rig manager until you manually re-sort by date. It should be very simple, and should be the default behavior, to have a flag in rig manager that simply re-sorts when a state change is detected on the profiler.