[2022] Two questions:

The Year 1 Pass does indeed begin with Season 1: Zero Hour.

Unsure on the second question, there are a couple of ways I can answer this for two different things. Bear with me!

1. Players that reach S-Tier should still earn XP at the same rate as players that are below Rank 100. You will always get 1000XP for a Tier 1 Ribbon, or 500 XP for a Tier 2 or Tier 3 Ribbon, in a sense. So something that we call "Grind XP" will always be ticking away and counting, while you play, to give you Battle Pass Points.
2. Weekly Challenges (outside of the Bonus Mission) exist for the entirety of a Season, so if you come in late - you'll have a load of challenges waiting for you to help progress through the Battle Pass tiers.
3. The Season 01: Zero Hour Badge is purely for Battle Pass Points Earned. So this is mostly involving the "Grind XP" (Passive play) and Weekly Challenges in order to gain that badge. You'll be needing 1,150 "Points" in order to unlock the Tier 1 mastery of it. All of that can be obtained by simply playing and also working towards your Weekly Challenges.

It's also worth noting that we're aware of an issue with the Season 1 badge, where it isn't counting your points correctly. This will be fixed in the next update and you should see the correct number of points you've earned since the launch of the Season.

Hey there, unfortunately, we had intended to have had this fixed in Update 1.2 and the intended fix had not worked succesfully. We have alerted the team on this and they are looking into options, but nothing to share at this moment in time.

We have updated our Known Issues page to reflect this.