1. What does 'diet' mean here?

It means hearing.

Attending a Criminal Court - Scottish Courts
https://www.scotcourts.gov.uk/taking-action/...a-court/atten...
Where the accused pleads not guilty a hearing, in summary cases called an intermediate diet, is set down a couple of weeks before the trial. This is to confirm ...

2.
How do we distinguish it with 'hearing' both in English and Chinese?
在英语里它们是同义词，不需要区分。只是其前的形容词（Intermediate, First， trial等）让其意思发生了变化。

在汉语里，hearing 本身就没有统一的译文，即使在法律界也是经常混用。见到的有听审，听证，聆讯（香港用法），美国的华人中甚至用“上庭”。而在大陆，最接近的对应词应该是“庭审/开庭/出庭”

First diet： 首次开庭
Intermediate diet：中期开庭

Hope this helps。