9-10 is really on the not enough side, and it may explain some molt. Ringnecks molt when the season of raising babies is done, before they have to look gorgeous for the next breeding season. In other words, summer, when the days are long and nights are short.
I know it's not summer in Ottowa! But, your light schedule is probably telling your bird it's time to drop feathers. It would be a good idea to provide more "nighttime" for your bird. If you never give more than 9-10 hours, you may find him doing a little molting almost all the time - untidy at best, this would not be healthy for him.
That "dust" you see is most likely the outter shell of the new feathers. They start growing protected by a little sheath, like the end of a shoelace. As the feather matures, this protective covering gets preened off. They look spikey until it's gone.
I think if you provide Pete a dish of water he should bathe himself when he sees fit. When you consider it, he's not really dirty anyway. He doesn't get splashed by mud or grimy hanging out inside trees. He's got a pretty sweet deal. If he likes getting a misting then that would be a fun thing for you to do together. But don't stress over bathing. He'll take care of it when he needs to, if you do your part by providing a tub.