1.
The first question is about the tense we should use after "as soon as". In a sentence such as this:
I had left when the phone rang.
you need to use the past perfect in the second clause to show which action came first and which – second. However, when you use “as soon as”, the sequence is clear and it is normally a matter of preference which one to use, so both your examples will be correct. In American English the preference would normally be past simple. The past perfect would emphasize the fact that one action was complete before the other one occurred. (an explanation given in Grammar for Teachers by Andrea DeCapua)
2.
In the second pair of examples they are both correct again. It is unnecessary to use past perfect because the time is mentioned and the sequence of events is clear. Also, the actions are described in the order in which they occurred. You can use the past perfect if you want, to emphasize that one was before the other.
3.
The third question was about the sentence
He said that the moment he first met her, he felt something special and began to keep a diary.
The actual words the man said must have been:
"The moment I first met her, I felt something special and began to keep a diary."
When you report his words and begin with “He said”, the entire phrase shifts one tense back and becomes:
He said that the moment he had first met her, he had felt something special and had begun to keep a diary.
Although this is the grammatically correct sentence, it is very common that the past simple does not become past perfect in indirect speech. When reporting, native speakers tend to make present tenses past ("I am studying" - "She said she was studying") but very often do not care to make the past tenses perfect, as grammar books always teach us we should.
That is what makes both these sentences correct: "He said that the moment he first met her, he felt something special and began to keep a diary." and “He said that the moment he had first met her, he had felt something special and had begun to keep a diary.” (have a look at the end of this page)
Although seemingly synonimous, these two uses can have different meanings.
In your examples, the first sentence expresses planning while the second one shows a general expectation/ promise.
First example:
Mary thought John was going to invite her to the party -> She thought he planned to invite her; she was on his guest list.
Mary thought John would invite her to the party -> She saw it as a logical, reasonable expectation that he did. expectation/ promise ( because they are good friends or because he said he would)
Second example:
- They thought the film was going to start at 8:00.-> They thought the film was scheduled to start at eight. - plan
- They thought the film would start at 8:00.-> They were told/they assumed that that was the time it started. - expectation/promise
Check some more examples and explanation of future in the past in this page
if you like. It's no grand authority as such, but there is some helpful information.
Best Answer
“I had better eat something” is not in past tense; it is a subjunctive modal expressing a recommendation. An englishpage.com article says the recommendation form of had better is used for future events; as in, for example, “You had better unplug the toaster before you try to clean it”, which would transform to “I had better unplug the toaster before I clean it”.
An englishgrammarsecrets.com article says: