From my memory of taking cases to Court, his past record may be considered at the sentencing stage.
That is still true. Previous convictions which are in any way relevant to the matter in hand can be taken as 'aggravating' factors, after determining the 'Starting Point" of a Sentence.
All Court Hearings are a matter of Public Record so available to anyone. If the Press are they they may report it.
That is also correct, but there is very inconsistent recording of proceedings, and transcripts are not normally produced. It is prudent for the parties to a hearing to provide their own verbatim report, the only definitive Court record in a Magistrates' Court will be the Clerk's notes, and while these can be copied for the parties on request, are hardly going to be comprehensive.
Higher Courts have a much higher standard of transcription which, with few exceptions, are available on request (often subject to a small admin fee).