Die man wacht buiten op zijn dochter.

Usually, die man means that man.

• de man = the man
• die man = that man

However, in real conversation, die can also point back to someone already mentioned, a bit like that in English.

Because man is a de-word in Dutch:

• de man
• die man

For singular nouns:

• de-word → die / deze
• het-word → dat / dit

So you get:

• die man = that man
• dat huis = that house

wachten op means to wait for.

This is a very common Dutch verb + preposition combination:

• Ik wacht op de bus. = I’m waiting for the bus.
• Zij wachten op hun vriend. = They are waiting for their friend.

So in your sentence:

• Die man wacht ... op zijn dochter.
• That man is waiting ... for his daughter.

Because Dutch often keeps the object together with its preposition:

• wachten op zijn dochter

The sentence structure is:

• Die man = subject
• wacht = finite verb
• buiten = adverb
• op zijn dochter = prepositional phrase

So op stays with zijn dochter, not right after wacht.

No, not in the same way as a true separable verb like opstaan.

• opstaan → Ik sta op.
• wachten op is better understood as verb + fixed preposition

So op belongs to the phrase op zijn dochter, not to the verb as a split-off particle.

Because Dutch often puts short adverbs like buiten before longer prepositional phrases.

So this order is very natural:

• Die man wacht buiten op zijn dochter.

It sounds like:

• subject → verb → place/manner adverb → prepositional phrase

Other orders are possible in some contexts, but this one is very normal and neutral.

Here buiten means outside.

It is an adverb in this sentence.

• Hij wacht buiten. = He is waiting outside.

It can also sometimes be part of other expressions, but here it simply tells you where he is waiting.

Because zijn refers to the owner, not to the gender of the noun.

• zijn dochter = his daughter
• haar dochter = her daughter

Since the subject is die man, the sentence uses zijn:

• Die man wacht buiten op zijn dochter.
• That man is waiting outside for his daughter.

The fact that dochter is female does not change the possessive pronoun.

Because the possessive pronoun already takes that slot.

In Dutch, you normally say:

• de dochter = the daughter
• zijn dochter = his daughter

You do not say zijn de dochter.

So zijn replaces the article here.

Dutch often uses the simple present where English uses either:

• waits
• is waiting

So:

• Die man wacht buiten op zijn dochter.

can mean:

• That man waits outside for his daughter or, more naturally in English,
• That man is waiting outside for his daughter

Dutch does have a progressive form like is aan het wachten, but it is not required here.

Yes. That would mean The man is waiting outside for his daughter.

The difference is:

• de man = the man
• die man = that man

So the original sentence is more demonstrative: it points out a particular man.

A few useful pronunciation notes:

• buiten: the ui sound is a famous Dutch vowel that does not exist exactly in English. It can be tricky for learners.
• dochter: the ch is the Dutch guttural sound, like in Scottish loch, not like English church.

Very rough guides:

• buiten ≈ something like BOW-tuhn, but with a Dutch ui sound instead of English ow
• dochter ≈ DOKH-ter, with a throat sound in ch

Yes, die can mean both:

• that for singular de-words
• those for plural nouns

Examples:

• die man = that man
• die mannen = those men

In your sentence it is singular because man is singular.