اگر او دیر بیاید، من دیگر منتظر نمیمانم.

Because this sentence is talking about a possible future situation, not a fact.

After اگر in this kind of conditional sentence, Persian often uses the present subjunctive.
So:

• بیاید = he/she come / if he/she comes
• It comes from آمدن = to come

In English, we say if he comes late. In Persian, the verb in that if-clause is often subjunctive:

• اگر او دیر بیاید = if he comes late

So بیاید does not mean past tense here. It is the normal form for a future/uncertain condition.

بیاید is the 3rd person singular present subjunctive of آمدن.

A simple breakdown:

• infinitive: آمدن = to come
• present stem: آی
• subjunctive prefix: بـ
• 3rd person singular ending: ـد

So:

• ب + آی + د = بیاید

This gives he/she may come or, in a sentence like this, if he/she comes.

Because می‌آید is the present indicative, which usually sounds more like:

• he comes
• he is coming
• he comes habitually

In a real future condition after اگر, Persian usually prefers the subjunctive:

• اگر او دیر بیاید = if he comes late

Using می‌آید after اگر is not the normal choice for this kind of sentence.

Here دیگر means something like:

• any longer
• anymore
• no longer

So:

• من دیگر منتظر نمی‌مانم = I won’t wait any longer / anymore

In negative sentences, دیگر often adds the idea of stopping something from this point on.

Compare:

• منتظر نمی‌مانم = I won’t wait
• دیگر منتظر نمی‌مانم = I won’t wait anymore / any longer

Yes, ماندن by itself usually means to stay or to remain.
But Persian often makes verbs with a non-verbal element + a light verb.

Here:

• منتظر = waiting / expectant
• منتظر ماندن = literally to remain waiting
• natural English meaning: to wait

So منتظر ماندن is a very common Persian way to say to wait.

نمی‌مانم is the 1st person singular present indicative negative of ماندن.

Breakdown:

• present stem: مان
• negative prefix: نـ
• imperfective/present prefix: می
• ending for I: ـم

So:

• ن + می + مان + م = نمی‌مانم
• meaning: I do not stay / I do not remain
• in this sentence: I do not wait

In standard spelling, it is usually written with a half-space:

• نمی‌مانم

You may also see it typed without the half-space as نمیمانم, especially informally online.

Persian often expresses ideas with compound verbs rather than one simple verb.

For to wait, several patterns exist, but منتظر ماندن is very common and natural.
So Persian does not always match English word-for-word.

Instead of one basic verb, you often get:

• a noun/adjective element: منتظر
• plus a light verb: ماندن

This is a very important pattern in Persian grammar.

Not always.

Persian verbs already show the person, so the subject is often omitted when it is clear from context.

So these can both work:

• اگر او دیر بیاید، من دیگر منتظر نمی‌مانم.
• اگر دیر بیاید، من دیگر منتظر نمی‌مانم.

Including او can make the sentence clearer or more emphatic, especially in writing.

It can mean either he or she.

Persian does not normally mark gender in third-person singular pronouns. So:

• او = he or she

You understand which one is meant from context.

دیر is an adverb meaning late.

It comes before the verb:

• دیر بیاید = come late / arrive late

This is the normal placement. Persian adverbs often come before the verb they modify.

Because Persian very commonly puts the if-clause first:

• اگر او دیر بیاید، من دیگر منتظر نمی‌مانم.

This is natural and common. It matches English pretty well:

• If he comes late, I won’t wait anymore.

You can sometimes move clauses around for style or emphasis, but the version with اگر... first is the most straightforward.

In writing, a comma after the if-clause is very common and helpful:

• اگر او دیر بیاید، من دیگر منتظر نمی‌مانم.

It separates the condition from the main clause.
In less careful writing, people may omit it, but using it is a good habit.

This version sounds standard written Persian and is also perfectly understandable in speech.
But in everyday conversation, people often use more colloquial forms:

• اگر → اگه
• او → اون
• بیاید → بیاد
• دیگر → دیگه
• نمی‌مانم → نمی‌مونم

So a conversational version might be:

• اگه اون دیر بیاد، من دیگه منتظر نمی‌مونم.

The sentence you were given is the more standard form.

A rough pronunciation is:

• agar u dir biyâyad, man digar montazer nemimânam

A few notes:

• اگر = agar
• او = u
• دیر = dir
• بیاید ≈ biyâyad
• دیگر = digar
• منتظر = montazer
• نمی‌مانم ≈ nemimânam

In casual speech, the pronunciation often becomes closer to:

• age un dir biyâd, man dige montazer nemimunam

Usually, it does not need to.

English sometimes says:

• If he comes late, then I won’t wait.

Persian normally just says:

• اگر او دیر بیاید، من دیگر منتظر نمی‌مانم.

The relationship between the two clauses is already clear from اگر, so an extra word meaning then is usually unnecessary.