Destiny 2 – Do PS4 and Xbox One Clan Players Contribute to Clan XP?

I haven't tried doing it with only 4 but with my experience doing it normal I don't believe it's possible. I've tried doing it multiple times after one person has fallen off and keep going with only 5 and it will end up stopping and you can't continue.

There are multiple videos showing how it's possible to skip parts or to do it solo, by using swords and supers to jump the gaps between reactors, but these will only get you to the last area with nothing happening. You have to get to the last plate on each section and have the "reactor temperature rises" message appear for each to actually progress and have the enemies spawn at the final area.

Yes many different game modes are locked behind the campaign.

The crucible unlocks first, only a mission or two into the game. Basic strikes and patrol missions unlock later once you have all 3 vanguard mentors reunited. And end game activities such as nightfalls and raids are, as the name suggests, only unlocked after the campaign is completed.

These will have to be done on each of your character slots or redone if you delete one.