I can't start the Infinite History in the time next
You need to have a Mentor selected to start the Infinite History Scenario.
How can I get the Tokipedia?
Tokipedia unlocks once you finish the Infinite History Story (you can check which characters you still need to complete each scenario with)
How can I access the opposite story on the Tokipedia?
You need to complete the story twice to unlock both story routes