In writing, it all depends on who your audience is. In personal e-mails and letters I will write don’t, can’t, doesn’t, etc., but in a business letter that would be a no-no and I would always spell the words out. Business writing is considered more formal.
In e-mail it can be less formal and if writing an internal e-mail I would use a short form, but when writing an e-mail to a client outside of my company I would be more formal and write the words out.
I would only use short forms like GB, OMG, LOL etc. in personal emails.
If I am transcribing a dictation and my boss says the word “don’t” in a sentence, I automatically change it to “do not” and I know he expects it of me. My job as the assistant is to make the letter look professional and that includes correcting grammar, spelling and punctuation when necessary.