Is it possible to even Open Adsense in a new window? I saw it sometime before but I am not able to see it now.
Thats not possible and it was never possible. Probably you saw it in Adwords but Adsense always had this feature in everybody's wishlist for years now.
Its possible now to do it With Google Ad manager. Import your Adsense Code into Google Ad manager Have the option in Google Ad manager to open the urls in new Window. Now you would see Adsense Opens in new Window See here