formal and informal request and apology strategies

I'm looking for sources that introduce different request and apology strategies.
I would like to know how American and English people request and apologize in formal and informal situations.

As for requests, it depends on what you're asking for. As for apologies, "I'm sorry" works in every situation.

Would you help me with this?

Can you answer my question?

Can you help me?

Would you loan me some money?

tulipflower said:

I'm looking for sources that introduce different request and apology strategies.
I would like to know how American and English people request and apologize in formal and informal situations.

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You mean we use different modals (would, ca, could) considering the importance of what we want to request for

No, the modal changes based on the relationship with the person and the degree of politeness, as well as whether it's truly a request or simply a polite way of giving a command.

I could call out to my husband "Hey, honey, what time is it?"
To a stranger in a casual setting, I might say "Excuse me, could you tell me the time, please?"
To my child at the dinner table, I may say "Pass the salt, please."
To a guest at the dinner table, I may say "Would you please pass the salt?"

tulipflower said:

You mean we use different modals (would, CAN, could) considering the importance of what we want to request for

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Just say "request" and not "request for".

You can make a request that's in the form of a statement. Example:

I have a question.