Despite what you may have been told in school, abbreviations, acronyms, and initialisms are commonly used in formal writing (though more often in business and the sciences than in the humanities). Exactly how they should be used depends on your audience, the country you're living in (British and American conventions differ), and the particular style guide you're following.
Here, in response to some of your questions, are ten brief guidelines for using and punctuating abbreviations. . . .
For the complete article, see Ten Tips for Using Abbreviations in Formal Writing.