Oh, man.. sorry for you and your dog.
Unless they have changed it in the last couple of years.. yes. the 20-50 is still SG rated.
Correct. When you pull in the clutch lever, the 2 clutch plate and intermediate plate splines are free to rattle back and forth on the splines of the transmission input shaft. Not much, mind you, but that is what you are hearing. If done for long enough, it will wear a flat spot on the input shaft and cause you some grief. Bump it into neutral at stop lights, etc. When you let out on the clutch lever, the springs will hold all those parts tightly and no wear will take place.
That is another reason to keep the rpms up at idle. There will be less shaking when the clutch lever is pulled in.