Non-core stuff = instanced or "open"?

My friend and I are about to get the expansions+living story and we'd really like to play together.

My question is... can we? Is it the same as personal story where one character is the instance owner and the other one just tags along? Or can we both do everything? We both get rewards even if one of us is the instance owner, right?

You definitely can play together, and mostly it works as you expect: one player is the instance owner, and the other tags along. When the first player enters an instance, a pop-up will appear in the middle of the other player's screen asking if they want to join. Every now and then (usually at the end of an instance, but occasionally part way through, at least in the Living World instances) it will ask the player who isn't the instance owner whether they want to accept the progress. If they say yes then they will get the same rewards as the instance owner.

There are a few of things to watch out for though:

1. If you're not up to the same story step in your story journal as the instance owner, you can join but you won't get the rewards. If you play through every instance together, this won't be a problem - but it will be if one of you skips ahead without the other.
2. If you're in a party with someone in the open world, your story journals don't synchronise in any way. So if their story journal is set to a different story step from yours, you'll see different things marked on your maps.
3. Some instances are designed for one player. In those cases anyone except the instance owner will typically be transformed into something with a set support ability rather than their normal abilities. I can't really say any more than that without spoilers. Instances where this happens are very rare (I can only think of three, and I've played most of the story instances from HoT onwards with my brother).

Thanks for the explanation, especially point one. This kind of ties in with a follow-up question I have. So if we decide that one of us is always the instance owner (which, to me, is unfair), we should be fine... but what about if we alternate, are we still OK? So for example I'm instance owner in the first instance, he's owner in the second, we still have synced progress and we can continue and get rewards... right?

At the end of each instance, the not-owner is asked if they want to progress to the same point. As long as that is done you are on the same track and can alternate as much as you want.

Nice, thank you. We played through Factions and Nightfall together like this and it was a blast, I'd hate to forfeit that experience. Thank you!