Currently no unless your logo is a text symbol.
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 Copy that, paste in status
A status on facebook is what are you doing right now or your main message on your facebook homepage.
Yes, it should. As you can see from the 'Terms' on the Facebook site, 'Facebook' is always capitalized. The logo has nothing to do with if it should be capitalized or not. Facebook is a proper noun, therefore you capitalize it. It's odd that people would think otherwise, because you wouldn't put something in all caps just because the logo is in all caps, would you?
Closest I could match was 7455 C
A deleted Facebook status can only be retrieved under unusual circumstances with the assistance of administration. It is necessary to write in with all the salient information and the request.