Greetings sagobro, and welcome to the Forums. Congrats on your new BlackBerry. To stop your duplicate gmail problem, read the link listed here "How do I stop duplicate gmails to my BlackBerry" Main Page - BlackBerryFAQ
Or you could just click on "hide sent messages" in your mailbox/options/general options section. That way they are still available on your bb if you need to find one at some point by just unhiding them again.