I know with my pool, and my buddy's pool, we have no way to turn the return valves off. These feed directly from the filter to heater and then out. If you could shut this off, then you could accidentally shut it off when it was running and build up a ton of pressure as you pull water and and offer no route out. So to answer that question, I would say you should leave the return line open. Normally you also leave the filter plugs open/top open (or at least not retightened). My buddy also loosens up any pipe connections he has (like the pipe going into and out of the heater, he opens to drain and leaves it open.
The drain valve should be closed, and we both close our skimmer valve as well. For mine, the skimmer and drain meet at a single valve, so it goes from drain off/skimmer open to blow that out, then skimmer off/drain open to blow the drain lines, then skimmer off/drain off together to keep both closed. My buddy has 2 individual lines with a single valve on both. When they're clear, he closes them off, plugs the skimmers, and leaves the valves closed. We unplug the skimmer plugs after the valves are closed to add in the antifreeze. I think because you have both ends closed and antifreeze in the line, it just makes sure the antifreeze doesn't make its way out somehow.
I'd be interested to hear why anyone would reopen the valves after they're done. If you can close the return line, I suppose you could do that just as well to make sure nothing gets back into the return pipes, but again, I can't close my return valves completely.
