Punctuation – How to Use Punctuation Around Abbreviations

It depends on the type of abbreviations. USA is an initialism, and as such, does not require periods. The style of acronyms and initialisms no longer requiring periods is now becoming more prevalent.

Abbreviations, generally, still require periods (e.g. Prof. — Oh, and e.g.) Although there are exceptions, especially in British english usage, as noted in your linked related question.

Which abbreviations take periods and which do not is variable depending on the style guide followed.

Never use such abbreviations especially when writing to your customer, no matter how close you are with them. Apart from sounding casual, you also risk the possibility of the client inferring you're too busy (to write complete words) even for your customers. How I hate it when people sign off with a BR (=best regards, supposedly).

Having said that, I think it's perfectly valid to use abbreviations that expand to nouns, such as WHO, FBI, WWW etc, and some latin derivatives such as N.B. and P.S.