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If you have installed BBM 7 then once you login to your BlackBerry ID on your device your BBM contacts will be restored back , Also check this Article My contacts and groups are missing
Regarding BlackBerry World , it you are unable to locate the icon then first uninstall BlackBerry world from Options > Device > Application Management > Locate and delete BlackBerry World , then perform another Battery pull restart .
Then From your BlackBerry Browser browse to or Click here http://mobileapps.blackberry.com/devicesoftware/entry.do?code=appworld3 to download version 4.0.0.55 . In addition check this Knowledge Base for further help :
KB29422 BlackBerry App World icon is missing after upgrading to BlackBerry App World 4.0.0.63 to 4.0.0.65.
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