No, Facebook does not have a trademark for the word "BOOK".
Yes, common words can be trademarks. Are you not aware of any of the following trademarks?
APPLE for computers. As a generic word for a fruit, it is not a trademark, but it is a famous trademark for computers.
TIDE for detergent. As a generic word for what the oceans do every 12 or so hours, it is not a trademark. But it is the leading brand of laundry detergent in the US.
COKE for a beverage. As a processed coal fuel, or a common word for cocaine, it is not a trademark. But it is probably one of the most recognizable trademarks on earth for a beverage. Even
COCA-COLA just a combination of the names of two plant extracts, coca and cola, from which it was originally made. That one started out as purely descriptive, but became distinctive over time with consumer recognition.
BUD for beer. As a short name for 'buddy', or as the sprout of a flowering plant, it is not a trademark. But it is one of the most famous beer trademarks in the US.
AMERICAN,
UNITED,
DELTA, or
VIRGIN? All common words, and all trademarks for airlines.
MONSTER for an energy drink.
Have you really never heard of any of those well-known brands?
I thought that common names cannot be trademarked.
Take a look around you at the trademarks you encounter in your daily life.
I'm always surprised at how many people say "dictionary words can't be trademarks" but somehow manage not to notice any of the trademarks which they see over and over again.