How does a student's misconduct history carry across to other courses (if it does)? Is there a difference between minor and major offences?
My UK university centrally tracks all academic offences, both major and minor, and I think this is pretty common. We are not allowed to release information about academic offences to employers or other universities. If the new course is at a new university, it is up to the applicant to inform the university. There may be a question on the application and the applicant must answer it truthfully. If the new course is at the same university, it depends on how well they track things, in this case, how well they tracked things in the past.

Past occurrences of academic misconduct are only used in deciding penalties for current occurrences of academic misconduct. Hopefully, a student would not commit academic misconduct again. If they did, the board may have discretion to ignore some past events if a large amount of time has elapsed. This is going to be specific to each board. Even if the board is allowed, discretion, they may not exercise it.