"Does that go as far as a full transcript of the proceedings?"
You might have to pay for a full transcription to be made. The judge and barristers will make their own notes ?in longhand but if the official reporter is using shorthand it will all have to be typed out from that. The official reporter would use the shorthand if asked to read back a reply but from one story I heard there didn't even seem to be any systematic preservation of the shorthand notes after the case had finished.
I'm not sure of the situation regarding audio recordings. They were being trialled back in one court in my day but it's a long time since then.