"過堂聆訊"是什麼意思?

我估你在說裁判署的過堂吧.
通常即是說提訊,
控方會話畀法官聽是否可以take plea(即問被告認唔認罪),
認咪求情囉.
如果唔認就排期審.
當然, 也可以是控方通知法庭未take得plea住而需要申請時間壓後案件至某年某月某日.
簡單來說, 就這樣子.

少少補充：(小弟只係copy自law dict,請大大見諒 )

曾就同一罪行被定罪或獲裁定無罪 (autrefois convict or autrefois acquit)
或者被控人可辯道，該法院不具有審訊他或她的司法管轄權

Mr LLL817 has answered your question in detail.

In English, 提訊 means "For Mention".  It means, there is some reasons to bring up the case.  It can be for any reason, like variation of bail conditions.

Is there one more function for Prima Facie estalished to the charges alleged for trial in a higher court?

I think you are sayiing committal.  I am not sure.  It seems that committal is also called 過堂 at some stage.  Anyway, 過堂 is  very vague expression.  I just wonder whether any linguist has studied the term, and can give us some insight.