Soggy:I don't know about ordering them by importance, but here are skills that I devote specific time to outside of regular dives...
basic air share
air sharing ascent simulating decompression stops
gas switches
mask removal and replacement
mask removal and ascent simulating decompression stops
mask removal and ascent with gas switch
lift bag deployment
lift bag deployment with air sharing ascent and simulated stops
toxing diver rescue with stops as necessary for convulsions
valve shutdowns
running line
following line maskless in touch contact
following line maskless in touch contact while sharing air
When possible, we try to do these skills mid-water with no visible reference.
Skills that get practiced all the time are mental games involving situational awareness (constantly switching attention between, equipment, team, & the environment), all the kicks, team communication (passive and active), buoyancy, etc, etc.
That's all I can think of in 5 minutes off the top of my head.
Now I'm going to go home and practice the "fiancee's birthday" skill.
FYI, S-drill is just a fancy name for safety drill, which just means fully deploying your long hose, switching to backup, restowing everything, then switching back to the long hose. Also include a valve drill in there or a modified valve drill (check that each valve is on). These drills are done at the beginning of every dive. In the ocean, I do them on my way to the bottom.
soggy: This all sounds a bit busy. I prefer a nice calm dive. I'm sure we now will hear from the "experts" on how we should all be diving.