All the above are common pronouncements from amateur grammarians, but none of them reflects English grammar or good writing. At best, grammar myths like these simply confuse formal English with standard English, assuming that because a grammatical construction is informal, it isn't standard English and is therefore "incorrect."At worst, they're flat-out wrong.
Writers would do well to remember the distinction between formal and informal language, and their relationship to standard English. Put simply, standard English can be both formal and informal. Here's how Huddleston and Pullum put it in (the highly recommended) A Student's Introduction to English Grammar:
Informal style is by no means restricted to speech. Informal style is now quite common in newspapers and magazines. They generally use a mixture of styles: a little more informal for some topics, a little more formal for others. And informal style is also becoming more common in printed books on academic subjects. We've chosen to write this book in a fairly informal style. If we hadn't, we wouldn' t be using we 've or hadn't, we'd be using we have and had not.In most writing contexts, strictly formal English sounds very odd. Failing to observe a rule of formal writing is not a failure to write standard English. More often than not, it's just good writing.