No, court proceedings are not in the public domain. You can attend the court when the trial is on and listen to what is said, you can take written notes ( as reporters do) but you can not record the proceedings on a tape recorder or similar.
Court proceedings ARE in the public domain - this means you can go to a court and listen and take notes. - alot of the time.
Records and transcripts are not.
Transcripts are made by come higher courts (not magistrates) and they will be available to the parties involved if there is an appeal. We dont get access to them.
Interesting cases are 'reported' and that is a summary of the case facts and the verbatim judgement. That may have some dialog but usually not much.
I've never tried it; all the transcripts I have ever had have been free to the lawyers; but I suspect that if you can find any agency which did a transcript of a trial for the court and lawyers, they would sell you a copy. The problem is that the expense would be enormous; even a three day trial has a full transcript running to a great many pages.
Incidentally, even the lawyers don't get a full transcript as a matter of course. What we ask for is an identified part of the transcript. This is usually just the judge's summing up but it may include some parts of the evidence and, in particular, rulings made by the judge on that evidence and any comments made by the judge in the course of the trial, which comments may be seen as improper or based on an incorrect reading of the law.