When upgrading your OS sometimes the option to install App World is not checked. If you don't check it for install you can download it from RIM's site: BlackBerry - Download BlackBerry App World
As for Hotmail, you might need to delete the account and then re-add it through Verizon's BIS portal. Hotmail and BlackBerry has been troublesome over the years. Google has done much more to insure BlackBerry integration. Microsoft has a vested interest in making your Hotmail experience much nicer on WP7 than on BlackBerry.