Nach der Sitzung hatte er endlich eine freie Stunde, und wir spazierten durch den Park.

Breakdown of Nach der Sitzung hatte er endlich eine freie Stunde, und wir spazierten durch den Park.

und
and
wir
we
haben
to have
er
he
nach
after
der Park
the park
durch
through
die Stunde
the hour
endlich
finally
die Sitzung
the meeting
frei
free
spazieren
to stroll
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Questions & Answers about Nach der Sitzung hatte er endlich eine freie Stunde, und wir spazierten durch den Park.

Why is nach followed by der Sitzung and not die Sitzung?
nach is one of the prepositions that always takes the dative case in German. The noun Sitzung is feminine, so its dative article is der (not die). Hence nach der Sitzung.
Why does the sentence begin with Nach der Sitzung, and why isn’t there a comma after it?
German main clauses allow different elements in the first position (the “Vorfeld”). Starting with the time expression Nach der Sitzung sets the scene (“after the meeting”) and is very natural. Simple adverbial phrases like this are not separated by a comma—only subordinate clauses or lists usually are.
Why is the verb hatte in the Präteritum (simple past) and not in the Perfekt (like hat gehabt)?
In written or formal narrative German, speakers often use the Präteritum for haben, sein and many other verbs. The Perfekt of haben would be hat gehabt (e.g. er hat eine freie Stunde gehabt), which is less common in writing. So we use the simpler past form hatte.
Why is the adverb endlich placed after the subject and what nuance does it add?
endlich is a modal-time adverb expressing relief or impatience that something has finally occurred (“at last,” “finally”). In a German main clause, adverbs like endlich typically appear in the “middle field” after the finite verb and subject but before objects. Placing endlich there emphasizes that he’d waited for this free hour.
Why does eine freie Stunde have the adjective ending -e?
Adjective endings depend on gender, number, case and the preceding article. Stunde is feminine singular and here it’s the direct object (accusative). With an indefinite article (eine), the weak ending -e is used in accusative feminine. Hence eine freie Stunde.
Why is there a comma before und wir spazierten, and is it necessary?

Standard German does not require a comma before the coordinating conjunction und when linking two main clauses or items. The comma in the example is optional—used here to signal a slight pause or clearer separation—but you could drop it:
eine freie Stunde und wir spazierten durch den Park.

Why does the verb still appear in second position after und, instead of first?
Even after und, each new main clause must obey the Verb-Second (V2) rule. The conjunction itself isn’t counted as an element of the clause. So in und wir spazierten…, wir is element 1 and spazierten (the finite verb) is element 2.
Why is durch den Park in the accusative case?
durch is one of the so-called four accusative prepositions (durch, für, gegen, ohne, um). It always takes the accusative. The masculine noun Park has the accusative article den, giving durch den Park (“through the park”).
Why does the sentence use spazierten (Präteritum) instead of a spoken-style Perfekt like wir sind spazieren gegangen?
In written narrative, the simple past (Präteritum) is standard for many verbs, including movement verbs like spazieren. In everyday speech, you’d more often hear the Perfekt wir sind spazieren gegangen, but in a text or story wir spazierten is more concise and typical.
Could I replace Nach der Sitzung with a subordinate clause using Nachdem, and how would the word order change?

Yes. Using the conjunction Nachdem (“after”) creates a subordinate clause and sends its verb to the end. You’d get:
Nachdem er die Sitzung beendet hatte, hatte er endlich eine freie Stunde, und wir spazierten durch den Park.
This version is more formal and longer; the original nach + noun construction is shorter and common in everyday usage.