Is a question always a question?

as constructed, it is a question.

Use the question mark. It's still a question. The readers will know what the character means. Or else, say:

"I'm fine. Knock it off already."

I've seen that type of question-without-a-question-mark construction used in published works. Joan Didion (one of my favorite authors) uses it regularly to show that her characters are speaking with a certain inflection.

"What are you doing?"
When I read this, I hear the character's voice going up at the end of the sentence.

"What are you doing."
When I read this, I hear the character's voice coming out as sounding sarcastic, angry, or annoyed.

I don't know, I think as a reader it would distract me to see a question without a question mark.

Well due to the different ways you can write this you can make it a question or a command. If you want to keep it the way you have it just to keep a sense of characterization or personality to the story I'd have to go with question mark. My reason is because without even looking at the punctuation you used at the end I read it as though Jane is asking him to knock it off.

"Will you knock it off already?"
"Will you knock it off already."

Which looks right to you? I'd have to say the first one. Also about the comma.

"Will you knock it off, already?"
"Will you knock it off already?"

In my opinion I wouldn't use one. I don't know everything about commas so I can tell you for sure if you should or shouldn't use it but how I read it there is no pause in her voice and I think that might be how you should decide whether or not if you want to use it or not.

"Will you knock it off [pause] already?"
"Will you knock it off already?" [No pause]

Grammatically, I can honestly say I don't think a comma is needed unless you want a pause, but again, I don't know everything about commas.

In dialog, the rules bend like spaghetti. If it is not spoken as a question, with the rising inflection, I think the question mark is definitely out of place--whether or not the words would constitute a question in another context. The idea is to indicate how it is said, not pass a test. Same reason we use fragments.

In its meaning, it is recognised that something that is grammatically a question might be used to demand, describe or do other things. But they are still conventionally given the question mark.

I don't mind seeing the occasional grammatical question with a period at the end. Just don't overdo it, and don't use it at all when a question mark doesn't really affect the meaning much, like when we can tell from context how the words are said.

Like with every device, use sparingly.

Personally the lack of a question mark would stop me. It's constructed as a question, even if it's a command/request. Contextually there's no question it's not a question. But grammatically it still needs a question mark. I understand that in some modern literature the question mark is dropped in favor of a period or comma, but that doesn't sit well with me.

"What are you doing." just reads wrong to me.

Yeah. A question without a question mark draws attention to itself. At least, for me it does. I notice, "ohh, the author didn't user a question mark" instead of "nice dialogue."

I can hear it in my head, and I'm fine without a question mark. I utilize this myself at times (probably more than I should), so it doesn't jar me. Based on the responses above though it's apparently a style preference.

Regarding the comma, I'm iffier. I read it without the comma here, especially since the character is exasperated and not prone to use proper pauses in speech. But it could go either way.

I'm guessing the end answer is up to you!