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