2. Yes, eventually we'd like to have multiple groups in the same space just for this reason--I always think the interdisciplinary stuff is underrated.
3. Some of both, probably, but mostly we want to support people that the existing system does not support (e.g. people that are not yet famous)
1. Try set up a lab in Cambridge at some point down the road.
2. Pay particular attention to CS theory: it's (arguably) high-impact and very cost effective --you can practically fund an entire generation of researchers in a subfield for a fraction of the cost of, say, a major interdisciplinary initiative. See for instance what the Simons foundation is doing at Berkeley[1].
Best of luck with what you're doing. You can end up actually changing the world in this way.
A lot of the stuff in TCS is theory for the sake of theory, and one would want to avoid too much of this.
I'm particularly interested in any arguments that complexity theory is high-impact (beyond the very useful insight that there are some problems for which no polynomial time algorithm is known). I have a pretty good idea of the impact of cryptography and randomized linear algebra (sometimes considered CS theory), but am also interested in hearing about other fields considered CS theory with useful applications.
MA or UK, though? Both would be awesome, I think, but I don't believe YC has any offices outside the US at the moment...?