Homeserver admins (of all homeservers that federate given Matrix room) can see who (meaning: Matrix user id) you've talked to and when it happened. They cannot access the content of the messages itself, as it is protected by E2EE.
Matrix P2P has been proposed to circumvent this issue (by embedding a local Matrix server within the client), but I have not yet seen it "in the wild".
Yes, that's correct.