The CA just signs the certificate. They don’t have access to the private key, and thus can’t decrypt the key exchange.
The key exchange is the only thing decrypted by the private keys. From that point on, everything is encrypted and decrypted by the agreed upon cipher using the exchanged key, which is randomly generated for each session.
this only works, if the client doesn't know the server yet or disregards an already known key (you know, like SSH or web browsers telling you the key has changed)
They could pretend to be any domain, yes, but you asked about inspecting a TLS stream, and afaik, there’s no way to do that without the private key. Once the TLS handshake begins, there wouldn’t be a chance for a man in the middle, so that kind of attack would have to be done before the connection is established.
Technically, either side can request that the other generate a key and use that one, and it will cost an additional round trip. But generally in practice, each side generates their own key and tells the other side that it will be using that key.
Yes, those keys are for symmetric encryption, and yes, it’s for performance. It’s way faster to just exchange keys with asymmetric encryption rather than do the whole stream.
Also, I think you meant SSL, not SSH. SSH Uses a different key exchange protocol.