Answers revealed in the comments.
GAME 1
There are five permanently inhabited U.S. territories, one of which is American Samoa. The other four were possessions of three other countries, immediately prior to becoming U.S. territories.
GAME 2
Only two Star Trek characters are mentioned by name in titles of films in the Star Trek franchise. Name the only movie in the franchise that features both of those characters but does NOT include either of these characters in its title.
Game one answers:
Spain
Japan
Denmark
GAME 2 answers:
Star Trek Into Darkness