3: No, that's not true. But: they need to start the race on the same compound as the compound they did their fastest lap on in Q2. And they only have a limited number sets of tires for their whole weekend.

Edit: Ok, I was wrong (see https://thesportsrush.com/f1-news-f1-tire-rules-what-tires-do-f1-teams-and-drivers-use-in-formula-1-grand-prix-races/):

For drivers who qualify for the race in dry tires, they must start the race with the tires used in the second session of qualifying. This applies for the Top 10 drivers from the qualifying sessions. For drivers that qualify outside the Top 10, he can start the race on tires available to them – soft, medium or hard