Она винила его в задержке.

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

• она = she
• винил = masculine past
• винила = feminine past
• винило = neuter past
• винили = plural past

So Она винила его в задержке uses винила because the subject is она.

Винила is:

• past tense
• feminine singular
• imperfective

Its dictionary form is винить.

The imperfective aspect often suggests something like:

• she was blaming him
• she blamed him repeatedly
• the sentence presents the action as a process or situation, not as a single completed event

So this sentence can sound like she was blaming him for the delay or she blamed him for the delay, depending on context.

Because винить takes a direct object in the accusative case: винить кого? что? = to blame whom? what?

Here, the person being blamed is he/him, so Russian uses его.

For masculine animate nouns and pronouns, the accusative often looks like the genitive. That is why you get:

• он = he
• его = him

So:

• Она винила его = She blamed him

This is because of the standard Russian pattern:

• винить кого в чём

That means to blame someone for something.

So:

• кого? → the person blamed = его
• в чём? → the matter/cause = в задержке

After в in this pattern, Russian uses the prepositional case:

• задержка → dictionary form
• в задержке → prepositional

So although English says for the delay, Russian says literally something closer to blame him in the delay. It is just the normal Russian construction.

Yes. It is very useful to learn it as a set pattern:

• винить кого-то в чём-то

Examples:

• винить друга в ошибке = to blame a friend for a mistake
• винить себя в неудаче = to blame oneself for a failure
• винить правительство в кризисе = to blame the government for the crisis

Learning the whole pattern is easier than translating word by word from English.

They are close, but not always identical.

• винить = to blame, to hold responsible
• обвинять / обвинить = to accuse, sometimes more formal or stronger

So:

• Она винила его в задержке = she blamed him for the delay
• Она обвинила его в задержке = she accused/blamed him for the delay

In many contexts they overlap, but обвинить can sound more definite or formal, like making an explicit accusation.

Also note aspect:

• обвинять = imperfective
• обвинить = perfective

With винить, Russian often uses it mainly as an imperfective verb.

Because винила is imperfective, and that may be exactly what the speaker wants.

Imperfective can suggest:

• an ongoing action: she was blaming him
• a repeated action: she kept blaming him
• a background description: she blamed him, and that was the situation

If you want a single completed accusation, Russian more often uses обвинила:

• Она обвинила его в задержке = she accused/blamed him for the delay

So the choice is not just grammar; it also affects how the event is viewed.

Yes. Russian word order is more flexible than English, because the cases show the grammatical roles.

Neutral order here is:

• Она винила его в задержке.

But you could also say:

• Его она винила в задержке.
  This emphasizes him.
• В задержке она винила его.
  This emphasizes the delay / that issue.

The basic meaning stays the same, but the focus changes.

It can mean both, depending on context.

Задержка often means:

• a delay
• lateness
• a holdup

So в задержке could refer to:

• a delayed arrival
• a postponed process
• someone being late
• some kind of hold-up

The exact nuance comes from context.

The usual stresses are:

• она́
• вини́ла
• его́
• в заде́ржке

So the sentence is pronounced roughly:

• она́ вини́ла его́ в заде́ржке

Stress matters in Russian, so it is worth learning words together with their stress.

Because него is normally used after a preposition.

Compare:

• Я вижу его. = I see him.
• Я думаю о нём. = I am thinking about him.

In your sentence, его is a direct object without a preposition, so it stays его.

The preposition в belongs with задержке, not with его:

• в задержке = in/for the delay

So него would be wrong here.

Yes, sometimes.

Russian often drops the subject pronoun when it is clear from context:

• Винила его в задержке.

This can still mean She was blaming him for the delay, if the context already makes clear who she is.

However, including она is perfectly normal if you want to make the subject explicit or contrastive.

Yes, it is grammatically natural.

That said, native speakers might choose different verbs depending on context:

• Она винила его в задержке.
• Она обвиняла его в задержке.
• Она обвинила его в задержке.

All are possible, but they differ slightly in aspect and tone.

Your sentence is a good example of the pattern винить кого-то в чём-то.