I was surpised to hear from a Japanese coworker that using a question mark "?" (gimonfu) after the か particle is correct Japanese.
Which of these are NG?
In what context is each acceptable/appropriate?
All 3 are correct.
could appear in old and/or formal Japanese, where the question mark is often absent. Note that you would still need a punctuation then, probably a full stop: 「。」
and 3. will both appear anywhere and depend only on the level of formality of the conversation. Omitting the particle would make your question slightly more familiar (or, in some case, slightly more masculine-sounding).