A request is the action of asking for something formally and politely.
We can use 'can' or 'could' in a request, when we ask someone to do something.
"Can everyone be quiet for a minute, please?"
"Can/Could you help me?"
"Could you wait half an hour?"
"Could you please show me the way?"
'Could' is often more polite than 'can'.
We can also use 'Do you mind.....' or 'Would you mind.....' + v(ing)
Do you mind waiting a moment? - No, I can wait.
Would you mind explaining that again, please?
Will you send this letter for me, please?
Would you open the door for me, please?
A suggestion is a plan or an idea that you mention for somebody else to think about.
We can use 'Shall we...?' or 'Let's' to make a suggestion.
It's a lovely day. Shall we go for a walk? _ Yes, OK.
Let's play some music. _ Good idea.
We can also use 'could':
'We could watch this movie on TV tonight.'
We can also use 'Why don't...?':
'Why don't we go together?'
'Why not write to her?'