How can I eliminate duplicate notifications when I have a custom notification on a Gmail label?
In the main screen of the Gmail app, from the "overflow" menu (the three dots in the top-right), choose Manage labels. From there, select a label to get a new screen with that label's settings. From that screen, the Label notifications setting controls whether you get a notification for new mails in that label. If you turn it off for "Priority Inbox" and "Important", you'll only get the notification from "Inbox".