Nach dem Flohmarkt zahlen wir die Standgebühr.

Because nach takes the dative case when it means after in a time expression.

• der Flohmarkt = the flea market
• masculine singular dative article = dem

So:

• nach dem Flohmarkt = after the flea market

This is a very common pattern:

• nach dem Essen = after the meal
• nach der Schule = after school
• nach dem Urlaub = after the vacation

Because German main clauses usually follow the verb-second rule.

In this sentence, Nach dem Flohmarkt has been placed at the beginning. That first position counts as one unit, so the conjugated verb must come next:

• Nach dem Flohmarkt | zahlen | wir | die Standgebühr

So even though wir is the subject, it comes after the verb here.

Compare:

• Wir zahlen die Standgebühr nach dem Flohmarkt.
• Nach dem Flohmarkt zahlen wir die Standgebühr.

Both are correct. In the second one, the time expression is emphasized more.

Yes, absolutely.

Both versions are grammatical:

• Nach dem Flohmarkt zahlen wir die Standgebühr.
• Wir zahlen die Standgebühr nach dem Flohmarkt.

The difference is mainly focus:

• Nach dem Flohmarkt ... puts the time first, so it sounds a bit more like As for after the flea market...
• Wir zahlen ... nach dem Flohmarkt is more neutral and straightforward.

German is flexible with word order, but the finite verb still stays in second position in a main clause.

It is the accusative direct object of zahlen.

The verb zahlen here means to pay, and the thing being paid is the object:

• die Standgebühr = the stall fee / booth fee

So in this sentence:

• wir = subject
• zahlen = verb
• die Standgebühr = direct object

A useful detail: for feminine singular nouns, the article is die in both nominative and accusative. So even though die does not change here, the phrase is still functioning as the accusative object.

Because German very often forms compound nouns by joining words together.

Here:

• der Stand = stand, stall, booth
• die Gebühr = fee

Together:

• die Standgebühr = stall fee / booth fee

This is completely normal in German. English often uses separate words, but German usually combines them into one noun.

Also, the gender of a compound noun is determined by the last part. Since Gebühr is feminine (die Gebühr), the whole compound is feminine:

• die Standgebühr

Because nach is a preposition, while nachdem is a subordinating conjunction.

Use nach before a noun phrase:

• nach dem Flohmarkt = after the flea market

Use nachdem before a clause with a verb:

• Nachdem wir auf dem Flohmarkt waren, zahlen wir die Standgebühr.
• Nachdem der Flohmarkt vorbei ist, zahlen wir die Standgebühr.

So in your sentence, the part after after is a noun phrase (the flea market), not a full clause, which is why nach is correct.

They are similar, and in this sentence both can work, but there is a slight usage difference.

You can say:

• Wir zahlen die Standgebühr.
• Wir bezahlen die Standgebühr.

Both mean We pay the stall fee.

A rough guide:

• zahlen often focuses on the act of paying
• bezahlen often takes the thing being paid for directly as its object

Also:

• jemandem etwas zahlen = to pay someone something
• etwas bezahlen = to pay for something
• jemanden bezahlen = to pay someone

So die Standgebühr zahlen is very natural German, and die Standgebühr bezahlen is also possible.

Not necessarily.

Nach dem Flohmarkt simply means after the flea market. It tells you that the payment happens later than the flea market, but it does not by itself say how soon afterward.

Depending on context, it could mean:

• right after it ends
• later that day
• at some later point after the event

If you wanted to make immediately after clearer, German could use extra wording, for example:

• direkt nach dem Flohmarkt = directly after the flea market
• gleich nach dem Flohmarkt = right after the flea market

In normal German, a singular countable noun like this usually needs an article or some other determiner.

So:

• Wir zahlen die Standgebühr. = normal and correct

Without the article:

• Wir zahlen Standgebühr.

that sounds unnatural in standard German.

German uses articles more regularly than English in many situations, so learners often need to get used to that. Here, die is the normal definite article because a specific fee is meant.