Facebook

Privacy Settings
Account -> Privacy settings -> Personal information and posts

Don't leave any of these on "Everyone"

Account -> Privacy settings -> Contact information

Don't leave any of these on everyone except "Add me as a friend" and/or "Send me a message"

Account -> Privacy settings -> Friends, tags and connections

Don't leave any of these on "Everyone"

Account -> Privacy settings -> Applications and websites> Instant Personalization Pilot Program/Edit Settings

Uncheck "Allow".

Account -> Privacy settings -> Search

Change from Everyone to Friends of friends. Uncheck the allow for "Public search results"

Account -> Privacy settings -> Customize settings -> Friends can check me in to places -> Disabled

Create event as a business page
As Facebook changes their settings so often, this was valid at of Oct 30, 2011. To create an event as a business page, you have:

Edit Page (top right) -> Apps (middle left) -> Go to App (bottom)