Learn Hardcore Japanese: nihongo ga wakaranakute, sensei ni situmon wo simasita. - I didn’t understand Japanese, so I asked the teacher a question.

In Japanese, 分かる behaves like to be understandable / to be clear rather than to understand (something). Because of that, the thing that is clear / not clear takes が, not を.

日本語が分かる。
Japanese is understandable. / I understand Japanese.
日本語が分からない。
Japanese is not understandable. / I don’t understand Japanese.

If you said 日本語を分からない, it would sound unnatural or incorrect in standard Japanese. With 分かる, always use が for the thing understood / not understood.

Why is it 日本語が and not 日本語は? Could I say 日本語は分からなくて?

Both are possible, but the nuance changes.

日本語が分からなくて…
Focuses on Japanese as the specific thing you do not understand.
It often answers an implicit question like What is it that you don’t understand? → Japanese (is what) I don’t understand.
日本語は分からなくて…
Uses 日本語 as the topic (what you’re talking about in general).
It can suggest a contrast, like: As for Japanese, I don’t understand it (but maybe I do understand something else).

In your sentence, 日本語が分からなくて、先生に質問をしました。, が is completely natural and common. は is grammatically fine, but it adds a bit more of a contrastive or topic-like feel: As for Japanese, I didn’t understand it, so I asked the teacher.

What grammar form is 分からなくて? How is it related to 分かりません?

分からなくて comes from the negative form of the verb 分かる:

Dictionary form: 分かる (to understand / be understandable)
Negative plain form: 分からない (don’t understand / not understandable)
Adverbial -くて form: 分からなくて

-なくて is the te-form of an adjective-like negative. It is used to:

connect to another clause
express reasons or causes
link actions / states in sequence

Your sentence:

日本語が分からなくて、先生に質問をしました。
Literally: Because Japanese was not understandable, I asked the teacher a question.

Polite forms:

分かりません = 分からない in polite form (don’t understand)
You could also say:
日本語が分からなくて、先生に質問しました。 (mixing plain negative with polite past)
or
日本語が分からなかったので、先生に質問をしました。

So 分からなくて is the negative -て form, linking the reason (not understanding) to the action (asking).

Why do we use 分からなくて instead of a full sentence like 日本語が分かりませんでした plus another sentence?

Both structures are possible, but they feel a bit different.

Single connected sentence (natural, flowing):
- 日本語が分からなくて、先生に質問をしました。
  Because I didn’t understand Japanese, I asked the teacher a question.
Here, 分からなくて (te-form) directly links the first situation to the second. It’s compact and is often used in spoken and written Japanese.
Two separate sentences (more “chunked”):
- 日本語が分かりませんでした。先生に質問をしました。
  I didn’t understand Japanese. I asked the teacher a question.
This is also correct, but the causal connection is weaker and more up to context. It’s more like listing events one after the other.

The て-form is very commonly used to show a smooth connection or a reason, so 分からなくて here naturally means something like since I didn’t understand / because I didn’t understand.

Who is the subject in this sentence? Why isn’t I written?

In Japanese, subjects (and topics) are often omitted when they are obvious from context.

In 日本語が分からなくて、先生に質問をしました。, the implied subject is I:

(私は) 日本語が分からなくて、先生に質問をしました。
I didn’t understand Japanese, so I asked the teacher a question.

The 私は part is simply dropped because:

The speaker is talking about themself, which is the default assumption.
Repeating 私 all the time sounds unnatural in Japanese.

If the subject were someone else and that mattered, it would usually be mentioned:

彼は日本語が分からなくて、先生に質問をしました。
He didn’t understand Japanese, so he asked the teacher a question.

Why do we use に with 先生に? What does に mean here?

に marks the person you direct the action to in this kind of sentence.

In 先生に質問をしました, the pattern is:

[person] に質問をする = to ask [person] a question

So:

先生に質問をしました。
I asked the teacher a question.
(Literally: I did a question to the teacher.)

Here, に can be thought of as to, marking the indirect object / target of the action, similar to English ask a question to the teacher.

You’ll see the same pattern with other verbs:

先生に聞きました。 = I asked / listened to the teacher.
友だちにメールを送ります。 = I will send an email to my friend.

Why is it 質問をしました and not simply 質問しました? Is を necessary?

Both are correct:

質問をしました。
質問しました。

質問する is a suru-verb formed from the noun 質問 (question) plus する (to do). With this kind of verb:

You can say 質問をする (with を)
Or 質問する (without を)

The meaning is the same: to ask a question.

Using を is slightly more explicit that 質問 is the object, but in everyday speech, it’s very common to drop を with する verbs formed from nouns:

勉強をする / 勉強する (to study)
練習をする / 練習する (to practice)
質問をする / 質問する (to ask a question)

In your sentence, 質問をしました is polite and clear, but 質問しました would also be natural.

What is the difference between 質問する and 聞く when talking about asking a question?

Both can be used when you ask something, but they focus on slightly different things.

質問する
- Literally: to do a question
- Emphasizes the act of asking a question itself.
- Pattern: [person] に質問する = ask [person] a question.
Example:
- 先生に質問をしました。
  I asked the teacher a question.
聞く
- Basic meaning: to listen / to hear / to ask
- When used as to ask, it often emphasizes asking to obtain information.
- Pattern: [person] に聞く = ask [person] (about something).
Example:
- 分からないことを先生に聞きました。
  I asked the teacher about what I didn’t understand.

In many everyday situations, 先生に聞きました can replace 先生に質問しました and sound very natural.

What you generally do not say is 質問を聞きました to mean I asked a question; that actually means I heard a question. To say ask a question, use:

質問する / 質問をする
or (先生に) 聞く

What tense and politeness level is しました? Does it make the whole sentence polite and past?

しました is:

the polite form (ます-form)
of する (to do)
in the past tense (ました)

So 質問をしました = 質問をした in plain form = I asked a question (polite past).

In Japanese, once you use a polite form (like ～ます / ～ました) at the end of a sentence, that sentence is polite.

In 日本語が分からなくて、先生に質問をしました。:

分からなくて is plain, but it’s not the final verb; it’s just a connecting form.
しました is polite past and is the main, sentence-final verb, so the whole sentence is understood as polite past.

It’s very common to mix a plain -て form in the first clause with a polite ました in the second clause like this.

Does 質問 here mean one question or can it also mean several questions?

質問 by itself is number-neutral. It can mean:

a question
questions
the act of questioning

Context decides how we interpret it.

In 先生に質問をしました, the most natural English is I asked the teacher a question, but it could also be I asked the teacher some questions, depending on what actually happened.

If you want to be explicit:

先生に一つ質問をしました。
I asked the teacher one question.
先生に何個か質問をしました。
I asked the teacher a few questions.
先生にたくさん質問をしました。
I asked the teacher many questions.

Why is it just 先生 and not 先生さん? Don’t we usually add さん to people?

先生 is already an honorific title meaning teacher / professor / doctor (in some contexts). You do not add さん to it.

Correct: 先生に質問をしました。
Wrong / childish-sounding: 先生さんに質問をしました。

For people’s names, you often add さん:

田中さん (Mr./Ms. Tanaka)
山本さん

But with certain titles, you generally do not add さん, because the word itself already has respect built in:

先生 (teacher/doctor)
先輩 (senior)
社長 (company president) – usually: 社長, not 社長さん in polite speech

So 先生に質問をしました is the natural respectful way to say I asked my teacher a question.