Learn Hardcore Russian: Моё сомнение исчезает, когда учитель спокойно объясняет правило. - My doubt disappears when the teacher calmly explains the rule.

You could say Мои сомнения исчезают (my doubts disappear) if you want to emphasize multiple separate doubts. The singular just focuses on the overall feeling of doubt as one state.

Can I say Мои сомнения исчезают, когда… instead? Is that correct?

Yes, that is grammatically correct:

Мои сомнения исчезают, когда учитель спокойно объясняет правило.

Difference in nuance:

Моё сомнение исчезает – one general feeling of doubt disappears.
Мои сомнения исчезают – several doubts, maybe about different details, disappear.

Both are natural; the choice depends on what you want to emphasize.

Why is it исчезает, not исчезнет?

This is about aspect and meaning:

исчезать / исчезнуть is an imperfective / perfective pair.
исчезает (imperfective, present) describes a repeated or typical situation, or an ongoing process.
исчезнет (perfective, future form) would mean “will disappear (once, at some point).”

In the sentence, we are talking about a general rule or habit:

Моё сомнение исчезает, когда… = My doubt (typically) disappears whenever…

So the imperfective present исчезает is the natural choice.

Could I use пропадает instead of исчезает? Do they mean the same?

They’re close, but not identical:

исчезать – to disappear, vanish (more neutral and a bit more “formal”/bookish).
пропадать – to be missing, to go away, to get lost (a bit more colloquial, can sound less “elegant”).

You can say:

Моё сомнение пропадает, когда учитель спокойно объясняет правило.

This is understandable and natural, just slightly more colloquial in tone than исчезает.

Both verbs are in the present tense: исчезает and объясняет. But the sentence sounds like a general truth or habit. Is that normal in Russian?

Yes. Russian uses the present tense for:

actions happening right now
general truths / habits / regular situations

So:

Моё сомнение исчезает, когда учитель спокойно объясняет правило.
= My doubt disappears when the teacher calmly explains the rule (whenever this happens).

This is the habitual/generic present, similar to English “Water boils at 100°C” or “I feel better when I sleep enough.”

Why is there a comma before когда?

In Russian, когда introduces a subordinate clause of time. The rule:

A main clause + a subordinate clause introduced by когда are normally separated by a comma.

Here:

Main clause: Моё сомнение исчезает
Subordinate time clause: когда учитель спокойно объясняет правило

So the comma is required:
Моё сомнение исчезает, когда учитель спокойно объясняет правило.

Can I put the когда-clause first, like: Когда учитель спокойно объясняет правило, моё сомнение исчезает?

Yes, absolutely. That word order is very natural:

Когда учитель спокойно объясняет правило, моё сомнение исчезает.

Meaning does not change. The difference is in emphasis:

Starting with Моё сомнение исчезает focuses first on the result.
Starting with Когда учитель… focuses first on the condition or situation in which the doubt disappears.

Both orders are correct and common.

Why is учитель in the nominative case and not something like у учителя?

Because учитель is the subject of the verb объясняет:

учитель объясняет правило – the teacher explains the rule

The subject of a sentence in Russian is in the nominative case.

If you say у учителя, that’s genitive after у and means “at the teacher’s / the teacher has.” For example:

У учителя есть книга. – The teacher has a book.

So in this sentence, учитель must be nominative.

Why is it спокойно объясняет, not спокойный объясняет or спокойная объясняет?

Because спокойно is an adverb, and adverbs modify verbs.

спокойный – adjective (describes a noun): спокойный учитель – a calm teacher
спокойная – feminine adjective: спокойная девушка – a calm girl
спокойно – adverb (describes how someone does something): спокойно объясняет – explains calmly

You need an adverb to say “explains calmly”, so спокойно is the correct form.

Where can I place спокойно in the sentence? Is учитель спокойно объясняет правило the only option?

Russian word order is flexible. The most neutral version is:

учитель спокойно объясняет правило

Other possibilities:

учитель объясняет правило спокойно – puts extra emphasis on calmly.
спокойно объясняет правило учитель – strong emphasis that it is the teacher who explains calmly (more stylistic/poetic or contrastive).

All are grammatically correct, but the original order sounds the most neutral in everyday speech.

Why does правило look like the nominative form if it is an object?

Because правило is a neuter, inanimate noun, and for such nouns:

Nominative singular = Accusative singular.

In this sentence, правило is the direct object of объясняет and is in the accusative case, but its form happens to be identical to the nominative:

Nominative: правило – rule
Accusative: правило – (explains) the rule

Does правило here mean “a rule” or “the rule”? How do Russians express that difference without articles?

Russian doesn’t have articles, so правило by itself can mean:

a rule
the rule
even sometimes rules in general, depending on context.

To make it more specific, Russians can add words:

это правило – this/the rule (we’re talking about now)
это грамматическое правило – this grammatical rule

In your sentence, правило is naturally understood as the rule being explained in class (whatever is currently under discussion).

What’s the aspect of объясняет and could we use a perfective form instead?

объясняет is imperfective, from объяснять / объяснить:

Imperfective: объяснять – to be explaining, to explain regularly/habitually.
Perfective: объяснить – to explain once, to finish explaining.

Present tense exists only for the imperfective, so:

объясняет – explains / is explaining (habitually / right now)

You could say in a different context:

Моё сомнение исчезнет, когда учитель спокойно объяснит правило.
My doubt will disappear when the teacher calmly explains (finishes explaining) the rule.

There both verbs are perfective and refer to a single future event.

How do you pronounce the sentence and where are the stress accents?

Stresses (accented vowels in caps):

МоЁ сомнЕние исчезАет, когдА учИтель спокОйно объяснЯет прАвило.

Rough guide:

моЁ – mo-YO
сомнЕние – sam-NYE-nee-ye
исчезАет – eesh-che-ZA-yet
когдА – kag-DA
учИтель – oo-CHEE-tyel
спокОйно – spa-KOY-na
объяснЯет – ob-yas-NYA-yet
прАвило – PRA-vee-la