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)
My favorite usage of "get to" is in South Park:
STAN: Does this mean we have to go to church on Sundays again?
RANDY: No. It means we get to, son. It means... we get to.
It's used differently than in your example, but you can see the connotations that this phrase has. "Get to think" means that no one is forcing you or prompting you to think, it's just the natural thing you end up doing in that situation.
Best Answer
If you want to advise, then say "You'd better ...". If you want to instruct then you can say "You must ..." (or "You'll have to ...").
So both your examples are correct, but mean different things. I would only use "must" if I was in a position of authority. For example a teacher might tell her students that they "must do their homework", or when describing an external obligation "We must pick up the litter, it's the law!"
You would normally "tidy up" and not "clean" the picnic area, since a picnic is outdoors, and you can't clean the soil, but you can tidy up.