email writing

Write it whatever way you want

Email is intended to be quick and informal. There are no hard and fast rules.
I've just exchanged emails with my son and neither of us used either a salutation - hello or whatever - or anything at the end.
On the other hand, if I was sending an email to a business or to a stranger I would be more formal.

Hello Rocky, it depends to whom you are writing. So for example if it's someone formal like company manager I would always use dear X if it is a friend I may say Hi or maybe nothing especially if replying

I have the impression that starting with (e.g.) 'Daniel' alone is a US (and possibly Australian?) custom, whereas British English would say 'Dear Daniel', or 'Hello', or whatever.

Also, a native speaker would not say 'the needful' but 'what is necessary/required'.

Well, I am a well-educated native English speaker and, while I would never start a letter with anything but "Dear ...........", if I am writing a new email to a friend I just start it with the forename, continuation emails in any subsequent exchange not even getting that. I conclude with just my forename.

On the other hand, if I am writing to an organisation, I do put "Bonjour" and a name if that is appropriate, and I conclude with, say, "merci d'avance" and/or "bien à vous".

If it's a business email, and you're witing to the person for the first time, you should always use "Dear Mr./Mrs. Lastname" Once you have a thread going, you can be more personal, either "Dear Firstname" or just "Firstname".

Personally, I would never use "Hello Firstname", even in a casual email to a friend.

And you would never say 'please do the needful', you would as SOHCAHTOA noted above, say, "please do what is necessary"

As a native speaker and sometime teacher of English I have to disagree with both ANON and SOHCAHTOA.
Whilst 'needful' is not commonly heard, it is a perfectly valid word which I use from time to time. It is in all of my English dictionaries and none of them qualify it as being either 'informal' or 'slang'.

As another native English speaker, I'd have to disagree completely with KASSEISTAMPER.

"Needful" is a very rarely used form in British english, although it is relatively common in Indian english. I certainly wouldn't use it in business english in Europe or the U.K.

See point 4 here:
http://travel.cnn.com/mumbai/life/10-indianisms-652344/
or here:
https://en.wikipedia.org/wiki/Do_the_needful

@ANON
We'll have to agree to disagree.
"Needful" appears in both Chambers and Collins English dictionaries and Webster's American English dictionary. None of them refer to it as being either 'informal' or 'slang' nor do they imply any specific connection to Indian English. All 3 define it in the same way - something necessary or essential.
And I shall continue to use it as and when though I agree that I would not use it in a formal context.