Learn Hardcore Korean: jigeum seonsaengnimkke jilmunhaedo dwaeyo?

께 is the honorific dative particle meaning “to (someone respected).” With teachers, seniors, customers, etc., 께 is the safest and most respectful choice.
한테 is casual, everyday speech. 선생님한테 isn’t wrong when talking about the teacher to classmates, but avoid it when addressing the teacher directly.
에게 is neutral/formal and common in writing. It’s not impolite, but it lacks the honorific nuance that 께 gives. In speech to a teacher, 께 sounds better.

What’s the difference between 께 and 께서?

께 marks the indirect object “to/for/from (an honored person).” Example: 선생님께 말씀드렸어요.
께서 is the honorific subject marker. Example: 선생님께서 오셨어요. In the target sentence, the teacher is the recipient, not the subject, so 께 is correct.

If I’m talking to the teacher, should I say “선생님, 지금 질문해도 돼요?” instead of “지금 선생님께 질문해도 돼요?”

Yes. When speaking directly to the teacher, it’s most natural to address them vocatively and drop the dative:

선생님, 지금 질문해도 돼요? “지금 선생님께…” is still understandable but a bit redundant when the teacher is your listener. Use 선생님께 when asking someone else about asking the teacher.

What does the ending -아/어도 되다 mean here?

It expresses permission: “Is it okay if I…?” or “May I…?”

Pattern: V-아/어도 되다 (Even if I do V, it’s acceptable) → permission.
Negative: V-면 안 되다 (If I do V, it’s not allowed) → prohibition.
Similar phrases: …해도 괜찮아요?, more deferential …해도 될까요?, very formal …해도 되겠습니까?

How polite is 돼요? Would 될까요 or 되겠습니까 be better to a teacher?

…돼요? Polite but fairly direct (해요체).
…될까요? Adds tentativeness; sounds softer and more respectful.
…되겠습니까? Formal and deferential (business/official or very respectful tone). To a teacher, …될까요? is a great default: 선생님, 지금 질문해도 될까요?

Why is it spelled 돼요 and not 되요?

돼요 is the contraction of 되어요 (되다 + 어요 → 되어요 → 돼요). Spelling it 되요 is a common mistake. The same applies to negatives: 안 돼요, not 안 되요.

Can I use 질문해도 and 질문을 해도? Which is more natural?

Both are acceptable:

질문해도 uses the verb 질문하다 (“to question/ask a question”).
질문을 해도 treats 질문 as a noun plus 하다. They’re nearly interchangeable here. If you use 드리다 (humble “give”), you’ll keep the object: 질문을 드려도…

Should I use 질문하다, 묻다/물어보다, 여쭤보다, or 질문(을) 드리다?

질문하다: neutral “to ask a question,” common in class contexts.
묻다/물어보다: “to ask (someone).” Natural and common: 선생님께 물어봐도 돼요?
여쭤보다: humble verb for asking a superior; very polite: 선생님께 여쭤봐도 될까요?
질문(을) 드리다: humble “to offer a question” to a superior: 선생님께 질문 하나 드려도 될까요? All are fine; to be maximally respectful, use 여쭤보다 or 질문 드리다.

Why is there no subject like 저는?

Korean typically omits obvious subjects. Context makes it clear the speaker means “I.” You can add for clarity or emphasis:

지금 제가 선생님께 질문해도 돼요? (more explicit) But usually it’s omitted.

Could I say “…물어봐도 되나요?” or “…되나요?” What nuance does -나요 add?

…되나요? sounds like you’re inquiring about the rule/possibility in a neutral way (“Is it allowed/does that work?”) and is a bit softer than straight …돼요?
…될까요? feels a notch more deferential and tentative than …되나요? All three are polite; to a teacher, …될까요? is often preferred.

Can I use -ㄹ 수 있어요? for permission (e.g., 질문할 수 있어요)?

Not usually. -ㄹ 수 있다 expresses ability/possibility (“be able to”), not permission. For permission, use -아/어도 되다:

Permission: 질문해도 돼요? (May I ask?)
Ability: 질문할 수 있어요? (Am I able to ask?/Is it possible to ask?) — this can sound odd for permission.

Can I move the word 지금 elsewhere?

Yes, adverbs like 지금 are flexible:

지금 선생님께 질문해도 돼요?
선생님께 지금 질문해도 돼요?
선생님, 지금 질문해도 돼요? All are natural; choose based on what you want to emphasize.

Is 이제 okay instead of 지금?

Usually no. 지금 = “right now, at this moment.” 이제 implies a change of state (“now, as of now/anymore”), so it can sound off here. Stick with 지금 for “now.”

How can I soften this further to sound extra polite?

Add softeners or limiters:

선생님, 지금 질문 좀 드려도 될까요? (좀 softens the request)
선생님, 지금 잠깐 여쭤봐도 될까요? (잠깐 “for a moment”)
선생님, 질문 하나만 해도 될까요? (하나만 “just one”) These make the request gentler.

Do I need to add the honorific -시- anywhere?

No. -시- marks honorifics on the verb of the respected person’s action. Here, the action (asking) is done by “I,” so there’s no -시-. If the teacher were the subject, you’d use it:

선생님, 지금 시간 되세요? (Do you have time now? — honorific on the teacher’s verb)

Is there a more formal version for very official settings?

Yes:

선생님께 질문해도 되겠습니까?
선생님께 여쭤봐도 되겠습니까? These use the deferential -습니다 style and sound very respectful.