I've always had trouble understanding か (question particle) in casual speech. I read that in casual situations, か can be used to give the sentence an exasperated or sarcastic tone. Like in:
負けっかよ！ As if I'd lose!
I think that I understand that usage reasonably well. What confuses me however is when か is used with a sentence that clearly should be a question (i.e. it has a question mark or a question word). For example:
やってみるか？ Want to give it a try?
I believe I've read that か is unnecessary (and not used) in casual speech to ask a question and questions are simply conveyed through a rising intonation or the addition of の（だ）. Could someone explain how is the above sentence different in terms of tone or nuance from the same sentence omitting か 「やってみる？」?
Furthermore, on a similar note I believe, the sentence final particle combination のか？！ seems to occur frequently. I'm not really sure what to make of this one. I thought の might be the explanatory の but how can one both explain and ask a question? For example:
そんな嘘にオレがだまされっと思ってんのか！？ Do you think I'd be taken in by a lie like that?! (I'm not confident of this translation)
How would that sentence's meaning be affected if it were instead: そんな嘘にオレがだまされっと思ってんの！？ or そんな嘘にオレがだまされっと思ってんか！？
Thank you very much for reading my post to the end : ). I know this question isn't that specific but any and all help is appreciated. Thanks again!