Наш поезд задержался из-за тумана.

Because наш has to agree with поезд.

• поезд = a masculine singular noun
• in this sentence, it is the subject, so it is in the nominative case

So the correct form is:

• наш поезд = our train

Compare:

• наш поезд = our train
• наша машина = our car
• наше такси = our taxi
• наши поезда = our trains

Russian past-tense verbs agree with the subject in gender and number.

The subject here is поезд, which is:

• masculine
• singular

So the past-tense form is:

• задержался = masculine singular past

Compare:

• поезд задержался = the train was delayed
• электричка задержалась = the commuter train was delayed
• такси задержалось = the taxi was delayed
• поезда задержались = the trains were delayed

The -ся ending makes the verb reflexive, but in many cases it is not literally reflexive in the English sense.

Here:

• задержать = to delay something
• задержаться = to be delayed / to get delayed

So:

• Они задержали поезд. = They delayed the train.
• Поезд задержался. = The train was delayed.

In this sentence, задержался is the natural way to say that the train itself ended up delayed, without focusing on who caused it.

It can correspond to both, depending on context.

Very often задержался feels a bit like:

• got delayed
• ended up delayed

It describes an event that happened to the train.

If you want a more explicitly passive structure, Russian can also say:

• Поезд был задержан. = The train was delayed.

But in everyday Russian, поезд задержался is extremely natural.

Because Russian does not normally use a present/past form of to be the way English does in this kind of sentence.

English says:

• Our train was delayed

Russian simply uses the past-tense verb:

• Наш поезд задержался

The past meaning is already built into задержался, so no separate was is needed.

Because the preposition из-за requires the genitive case.

The base form is:

• туман = fog

In the genitive singular, it becomes:

• тумана

So:

• из-за тумана = because of the fog

This is a very common pattern:

• из-за дождя = because of the rain
• из-за снега = because of the snow
• из-за аварии = because of the accident

In this sentence, из-за means because of.

It is often used for a cause, especially when the cause is a problem, obstacle, or something undesirable.

So из-за тумана is very natural, because fog is the reason for the delay.

A useful nuance:

• из-за often sounds neutral-to-negative: because of, due to
• благодаря usually has a positive sense: thanks to

For example:

• из-за тумана = because of the fog
• благодаря помощи = thanks to the help

Задержался is perfective.

That means it presents the delay as a completed event or a single occurrence:

• the train got delayed
• the delay happened

If you used the imperfective, you would get something like:

• задерживался

That would suggest an ongoing, repeated, or background action:

• Наш поезд часто задерживался из-за тумана. = Our train was often delayed because of fog.
• Поезд задерживался уже час. = The train had been delayed for an hour already / was being delayed for an hour.

So in your sentence, the perfective form fits the simple fact that the delay occurred.

Yes, you could.

That version is grammatically correct and means roughly the same thing:

• Наш поезд задержался из-за тумана.
• Наш поезд был задержан из-за тумана.

But there is a difference in style and focus:

• задержался = very natural, everyday, event-focused
• был задержан = more formal, more clearly passive, often used in announcements or official language

So in ordinary speech, задержался is often the more idiomatic choice.

Yes. Russian word order is flexible.

The sentence:

• Наш поезд задержался из-за тумана.

is a neutral, natural order.

But you can also say:

• Из-за тумана наш поезд задержался.

This puts more emphasis on the cause: because of the fog.

In Russian, changing word order usually changes focus or emphasis, not the basic meaning.

The main stresses are:

• наш по́езд задержа́лся из-за тума́на

A rough pronunciation guide:

• наш = nash
• по́езд = PO-yezd
• задержа́лся = za-der-ZHAL-sya
• из-за = iz-ZA
• тума́на = too-MA-na

A couple of useful notes:

• поезд has two syllables: по-езд
• -ся is usually pronounced more like -sya than a full separate syllable

Because поезд is the subject of the sentence — it is the thing that was delayed.

In Russian, the subject is normally in the nominative case.

So:

• поезд = nominative singular

Meanwhile, тумана is in the genitive because it comes after из-за.

So the sentence shows two different case roles:

• поезд = subject, nominative
• тумана = object of the preposition из-за, genitive