Well, keep in mind that informal writing is inherently far more flexible than formal writing, and people simply won’t care very much whether you use a comma or not. So, the commas you’re asking about would all be optional in an informal letter.
The use of a comma after the salutation is still quite normal in formal American letters. Sometimes a colon is used in business letters. I’ve heard that the current trend in the UK is to omit the comma after the salutation, but I guess a Brit ought to confirm that for you.
I’d say that the use of a comma after your final closing phrase (the one right before your name) is also still standard for formal letter in the US.