What are the common greetings when writing to an acquaintance (not necessarily a close friend)?

Question

What are the common greetings when writing to an acquaintance (or someone not necessarily a close friend)? Is "how are you" or "how are you doing these days" too casual in writing ?

Or do I need a greeting before I talk about something else ?

My question is for the English writing exam for Chinese College Entrance Exam. In the past they had the writing exam like these:

1. Please write to your pen pal Peter in UK, telling him your uncle will be on a business trip to his city, asking some information about his city ...

2. Please write to an exchange student who stayed in your home last month and had returned to the US, asking his progress in Chinese learning and provides some advice for that.

3. A friend from UK will visit his Chinese friend next week so he wrote an letter to you asking about the guest etiquette in China. Please writing a response letter.

Answer 1

Begin with "Dear {name},

Write your letter using normal English. I'd suggest saying "I hope you're well" rather than "How are you?" unless the main purpose of your letter is to find out how the person is. It is not "too casual", but usually when you write to someone there is some other purpose. The letter can be written in a friendly style.

These are called "pleasantries". They are not part of the main purpose of the letter (They are not relevant to asking about the city) But they make the letter sound more friendly, and are very common in informal writing.

For the exam question, you can include them. They might or might not improve your mark. They should not lower the mark. But the letter must not only consist of pleasantries. You must proceed to asking about Peter's city, or whatever.

End with "Best Wishes" and your name. There are lots of other perfectly acceptable closing phrases, but this will work fine in most contexts.

Dear Peter,

I hope you are well and enjoyed the Chinese biscuits I sent you.

My uncle, Li Xingming, is going on a business trip to Brighton next month, and I'd like to ask you about the city...

...

Best Wishes

Quilang

Answer 2

This question requires more context. It depends heavily on how well you know the person and how formally you are writing to them. I was taught that the greeting was just the opening two or three words ranging from "Dear Sir or Madam" to "Hi Joe" and should usually match the closing phrase (that which comes before the signature) ranging from "Yours sincerely" to "Regards".
However, assuming this is not a formal or business letter or email then both your options are OK for casual missives.

Hi Joe,
How are you? [optional]
We are holding a reunion party next Wednesday and would love to see you there.
Regards,
John.

A formal letter would normally omit such pleasantries.

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Later after the OP's update.
I think James K has covered most of what I would have said in his answer. Based on the questions I would have said your relationship to the recipients is not that close, they are not family members or long term friends, so a formal but friendly approach is applicable as in Jame's example. My example was aimed at an old friend, say from school days.