This isn't quite right. Even with SR and the speed of light its possible to build consistent systems and achieve consensus. Not-eventually-consistent doesn't mean instantaneous. The SoL just sets a lower bound on the speed of consensus.
It's important to not overstate the importance of that bound, though.
Sure. CA fulfills that requirement. Of course, you throw away any semblance of partition tolerance.
Of course, a single machine guarantees there can be no partitioning, and really easy to obtain consensus. It might not be terribly fault-tolerant, however.
CA is a not really a valid/possible thing in the context of CAP. The original phrasing of the theorem was poor and the "choose 2" myth persists. You can choose to (or accidentally) give up C or A but you don't get to choose to not have partitions. Not being partition tolerant doesn't really make sense (you're just broken?) if partitions are going to happen. A better phrasing of CAP is "in a network with partitions a distributed system cannot be both consistent and available." (note: this doesn't guarantee that you are one of C or A, you just can't be C and A.) You can see that definition used in formal treatments, e.g. Theorem 1 in https://users.ece.cmu.edu/~adrian/731-sp04/readings/GL-cap.p...
(Briefly, note that the original article is critiquing that definition of availability in practice which is legitimate but not relevant to this sub-thread.)
What I'm saying is that EC is most definitely NOT a requirement of physics/the speed of light (what your original post claimed.) The speed of light only sets a (theoretical) limits on how fast you can implement a consistent system.
The original Paxos paper ("The part-time parliament") uses an analogy of a quorum of parliamentarians occasionally getting together in the the same building and agreeing on something. Of course it being the same building is arbitrary and doesn't actually matter, but it's easier to intuit that the speed of light isn't an insurmountable road-block at that scale.
It's important to not overstate the importance of that bound, though.