Na de groepsfoto volgt de toespraak.

Because Dutch uses verb-second (V2) word order in main clauses.

The first element in this sentence is Na de groepsfoto. Since that whole time phrase comes first, the conjugated verb must come second:

• Na de groepsfoto
  • volgt
    • de toespraak

So the subject de toespraak comes after the verb. This is often called inversion.

Compare:

• De toespraak volgt na de groepsfoto.
• Na de groepsfoto volgt de toespraak.

Both are possible, but when the sentence starts with Na de groepsfoto, the verb moves before the subject.

Na is a preposition, and it means after.

In this sentence:

• na de groepsfoto = after the group photo

Like English after, it is followed by a noun phrase.

More examples:

• na het eten = after the meal / after eating
• na school = after school
• na de vergadering = after the meeting

Because groepsfoto and toespraak are both de-words.

Dutch singular nouns take either:

• de
• het

These are mostly things you have to learn with each noun.

So:

• de groepsfoto
• de toespraak

This does not mean they are plural here. They are both singular nouns with the definite article de.

Yes. Dutch usually writes compound nouns as one word.

So:

• groep
  • foto → groepsfoto

This is very normal in Dutch. English often writes such combinations as two words, but Dutch usually combines them.

Other examples:

• treinstation = train station
• huisdeur = house door / front door
• tafelblad = tabletop

In groepsfoto, the s is a linking sound that often appears in compounds.

Volgt is the third person singular present tense of the verb volgen.

Conjugation:

• ik volg
• jij volgt
• hij/zij/het volgt
• wij volgen
• jullie volgen
• zij volgen

Here the subject is de toespraak, which is singular, so the verb is volgt.

Here volgen means something like:

• to follow
• to come next
• to take place afterwards

So in this context, it is about the order of events.

Dutch volgen can also be used in other ways, for example:

• De hond volgt mij. = The dog follows me.
• Ik volg een cursus. = I am taking/following a course.
• Kunt u mij volgen? = Can you follow me? / understand me?

In Na de groepsfoto volgt de toespraak, it has the sense of comes next in the program.

Yes, that is possible.

• Na de groepsfoto volgt de toespraak.
• Na de groepsfoto komt de toespraak.

Both can mean that the speech comes after the group photo.

The difference is mainly in tone and style:

• volgt sounds a bit more like schedule/order/program language
• komt sounds a bit more everyday and general

So volgt is very natural if you are talking about the sequence of an event.

Because in Dutch, a short introductory phrase like this usually does not need a comma.

So the normal spelling is:

• Na de groepsfoto volgt de toespraak.

A comma is sometimes possible for emphasis or style, but in ordinary writing it is usually omitted.

Yes. De toespraak is the subject.

A good clue is the verb ending:

• volgt is singular
• de toespraak is singular

So even though the subject comes after the verb, it is still the thing that follows / comes next.

This is common in Dutch after a fronted phrase:

• Morgen begint de cursus.
• Na de pauze start het concert.
• Na de groepsfoto volgt de toespraak.

In all of these, the subject comes after the verb because the sentence starts with another element.

Yes. That is grammatically correct.

Compare:

• Na de groepsfoto volgt de toespraak.
• De toespraak volgt na de groepsfoto.

The meaning is basically the same, but the focus is a little different:

• Na de groepsfoto... emphasizes the time/order
• De toespraak... emphasizes the speech itself

Dutch lets you move elements to the front fairly freely, but the conjugated verb still stays in second position in a main clause.

A rough pronunciation guide:

• groepsfoto ≈ khroaps-fo-to
• toespraak ≈ too-spraak

A few useful notes:

• g in standard Dutch is the throaty sound often written as kh or ch
• oe sounds like oo in boot
• aa is a long ah sound
• sp at the start of a syllable is usually pronounced like English sp, not shp

The stress is usually:

• GROEPSfoto
• TOEspraak

It sounds mostly neutral, but volgt gives it a slightly formal / program-like feel.

You might hear it in contexts like:

• an event schedule
• a ceremony
• an announcement
• a written program

For example, at a formal event, this sounds very natural:

• Na de groepsfoto volgt de toespraak.

In very casual speech, someone might be more likely to say:

• Na de groepsfoto komt de toespraak.