Adding the widget: touch and hold the Home Screen, tap Edit, then Add Widget, and search for Today in History. On the Lock Screen: touch and hold it, tap Customize, then Lock Screen, and add it below the clock or next to the date.
Another day: swipe sideways, use the arrows, or tap the date to pick any day of the year.
Offline: days you have opened before work without a connection, photos included. A new day needs a connection once.
The quiz: one round a day, the same photos for everyone (up to five; some dates have fewer). Play on consecutive days to keep your streak; it holds until the day is over.
Something wrong in an entry? The words come from Wikipedia's editors. Tap the entry, open its article, and you can suggest a fix there, or tell us.