Answers revealed in the comments.
GAME 1
What two-word term for a burdensome possession originates from a legend in which an angered Siamese king would give a certain gift to a rival, with the subsequent care of the gift driving the recipient to financial ruin?
GAME 2
Pomerania, a historical region in Europe with a name derived from Slavic meaning “by the sea”, and lends its name to a breed of dog, is split between two modern-day countries. Name one of those two countries.
Game one answer:
White Elephant
GAME 2 answers:
Poland
Germany