TL;DW, the questions/answers are below (a lot is paraphrased, but I think I got the general idea):
Q: Do you like our room?
A: Yeah, you did a really nice job on this. It looks nice
Q: Could you explain the strategy element in the new XCOM?
A: I think one of the points we want to make is that you focus on strategy in the base, and tactics in the field. We're bringing together a real-time, third-person view of our interpretation of the battlescape and being able to look around and say "What are my options here? Where can I move my agents? What powers do I need to use?"
Q: Is there any base building?
A: We've been throwing that around, but we haven't settled on something yet. We think it's a cool idea, so we'll try to implement it if possible.
Q: Any Psionics/Molecular Control tech?
A: We're still playing around with all the abilities, so there's some stuff that could be implemented, we don't know for sure yet.
Q: Are there random UFO encounters like in the original game (i.e. Interceptor missions)?
A: I don't know if we're going to do interception missions specifically, but there are crash sites that you can investigate. The game follows a linear storyline with side-missions that you can go on (eg. grab a Titan, get research).
Q: Where did the new alien designs come from and will we see the original aliens?
A: We've all seen the little grey men, little green men, and they're not that alien anymore. We're used to it. So how can we bring about something fresh and different? There's currently no plans for appearances by the original aliens.
Q: Will there be variety in aliens, how many enemy types are there?
A: We're not settled on a specific number now, but there's some subtle variations on the Outsider enemies and some things people haven't seen yet, but I'm not going to put a number on how many varieties of enemies there'll be.
Q: We know there's no competitive multiplayer, but what about co-op?
A: The game is a massively single player game. We're trying to give the player as much agency as possible. Adding co-op, while it can be cool, would involve a completely different approach to balancing, particularly in terms of "fear".
Q: Did Martin Slater's departure radically affect the game's direction?
A: To be clear, there's not much to say on Martin. He left, that's that. I think the direction overall has always been a team effort. While there has been significant changes from last year to this year, it had nothing to do with Martin.
Q: How is variety in the game?
A: The goal is to have a lot of variety, whether it's research, building your agents, getting new weapons, and we want to make that as robust as possible. We just want to give the player as many tools as possible to make the game experience fun for them.
Q: How long is the campaign?
A: We're not sure how long the game is going to be yet, but I know it'll at least be longer than 4 hours. We'll have a better idea of how long it's going to be as we get farther along in development.
Q: Are there plans for alien containment?
A: There was a point during development when that was part of the game, but we're not sure if it'll end up in the final game.
Q: Will there be more XCOMs?
A: The plan is always to make great games and figure out how to continue making more.