Is it possible to prevent all Internet websites, but allow just a few? (Blacklist websites, whitelist some?)

Yes, you can do this with PolicyPak Browser Router.

To do this, set up a rule (route) like what is seen here. Specify that the Internet Security Zone is set to BLOCK.

Set Policy Name And Block Internet Security Zone

Then, make other rules which route to the websites you want. Finally, ensure your blocking policy is LAST in the list, so all whitelist items will process before the BLOCK item.

PolicyPak Browser Router Screenshot