Yes. The rag is to form a partial seal, so all the water from the hose goes into the pipe. Watch when you do this, there may be a large glob of leaves etc come up in your skimmer.
This statement is inconsistent with a skimmer clog. If you indeed have a skimmer clog, the filter pressure would be lower and so would the flow rate.strong water movement yes.
This statement is inconsistent with a skimmer clog. If you indeed have a skimmer clog, the filter pressure would be lower and so would the flow rate.
Are you sure there isn't another valve or two splitting the suction to a drain or vacuum port?
I'd still do the water hose, just to see where the water goes back into the pool at.
I'd certainly ignore that Start and Clean Filter lettering. Never seen that before.