A: Playing the Ring to the table uses up one of your Plays, yes. Picking it up again to activate it by placing it face-out in your hand does not take up a play, and neither does turning it around again to face you, thus de-activating it, and returning it to your hand fully. From there it’s able to be re-played again, which would use up another of your official Plays.
So, yes, if you want to do that for as many Plays are allowed on your turn, just to burn up your turn without playing anything else, thus achieving the functional ability to “pass” on your turn, we’d have to admit that is allowed by the current wording of the card & rules.