Based on the themes and elements found in mythology and folklore surrounding Köğüdei Mergen, here are the answers to your questions:
What did Köğüdei Mergen cross on his journey? b) A poisonous sea
What did Köğüdei Mergen do after defeating Kara-Kula? a) Set all the people free
Who did Köğüdei Mergen marry? b) Altyn Küskü
Where did Köğüdei Mergen go to fight Erlik? b) The underworld
Where can Köğüdei Mergen and his companions be seen after their lives came to an end? a) In the stars
Please verify these answers with your study materials, as there can be variations in different adaptations or interpretations of the stories.