Learn Hardcore German: Am Samstag spielen wir im Park ein Freundschaftsspiel gegen den Nachbarn. - On Saturday we play a friendly match in the park against the neighbor.

an Samstag is simply wrong in standard German.
im Samstag (in dem Samstag) would only make sense in some very unusual, poetic context and is not how you talk about when something happens.

Why does the verb come before the subject: Am Samstag spielen wir and not Am Samstag wir spielen?

German main clauses follow the verb‑second rule:

The conjugated verb (here spielen) must be in second position in the sentence.
Only one element can stand before the verb (here the time phrase Am Samstag).

So:

Wir spielen am Samstag im Park … (subject first, verb second)
Am Samstag spielen wir im Park … (time phrase first, verb second, subject third)

Wir spielen am Samstag … and Am Samstag spielen wir … are both correct; the difference is just what you want to emphasize (neutral vs. slight emphasis on “on Saturday”).

Can I also say Wir spielen am Samstag im Park ein Freundschaftsspiel gegen den Nachbarn? Is the meaning different?

Yes, that sentence is also correct and has the same basic meaning.

Word order in German main clauses is relatively flexible for elements that come after the verb. Moving am Samstag to the front (as in the original) just puts a bit more emphasis on the time. Neutral, very common version:

Wir spielen am Samstag im Park ein Freundschaftsspiel gegen den Nachbarn.

Original version:

Am Samstag spielen wir im Park ein Freundschaftsspiel gegen den Nachbarn.

Both are natural.

What case is ein Freundschaftsspiel, and why ein and not einem or eines?

Freundschaftsspiel is a neuter noun (das Freundschaftsspiel).

In the sentence, it is the direct object of spielen → it’s in the accusative case.

Neuter ein‑words look like this:

Nominative: ein Freundschaftsspiel
Accusative: ein Freundschaftsspiel
Dative: einem Freundschaftsspiel
Genitive: eines Freundschaftsspiels

Nominative and accusative are the same for neuter nouns, so ein Freundschaftsspiel is correct as the object here, not einem or eines.

Why is Freundschaftsspiel written as one long word and not as Freundschafts Spiel or Freundschafts-Spiel?

German loves compound nouns: it often joins two (or more) nouns into one new noun.

Here:

die Freundschaft (friendship)
das Spiel (game, match)

→ das Freundschaftsspiel = a friendly match (literally: friendship‑game).

The whole compound is written as one word and is capitalized as a noun. A hyphen is sometimes used in very long or complex compounds, but Freundschaftsspiel is normally written without a hyphen.

What does gegen mean here, and why is it gegen den Nachbarn?

The preposition gegen means against.

In sports:
ein Spiel gegen jemanden = a game/match against someone

Gegen always takes the accusative case, so:

masculine: gegen den Nachbarn
feminine: gegen die Mannschaft
neuter: gegen das Team
plural: gegen die Nachbarn

So den Nachbarn is accusative singular, required by gegen.

Why is it den Nachbarn and not den Nachbar?

Nachbar is a weak masculine noun (also called an ‑n noun). These nouns add ‑n or ‑en in all cases except the nominative singular.

For der Nachbar:

Nominative singular: der Nachbar (subject)
Accusative singular: den Nachbarn
Dative singular: dem Nachbarn
Genitive singular: des Nachbarn

So after gegen (which requires accusative), we need den Nachbarn, not den Nachbar.

Does den Nachbarn mean one neighbor or several neighbors?

In this sentence it means one neighbor.

den Nachbarn = accusative singular masculine (article den tells you it’s singular)
die Nachbarn (with die, not den) would be the plural: against the neighbors

So:

… gegen den Nachbarn. → against the (single) neighbor
… gegen die Nachbarn. → against the neighbors (more than one)

Why is it im Park and not in dem Park? Are they different?

im is just the contracted form of in dem:

im Park = in dem Park (in the park)

Both are grammatically correct and mean the same thing. In normal speech and writing, Germans almost always use the short form (im, am, beim, etc.) unless they want special emphasis.

Here, im Park is standard and sounds most natural.

Why is Park in the dative case in im Park?

The preposition in can take either dative or accusative, depending on the meaning:

Dative for location (where something is):
im Park = in dem Park = in the park (location)
Accusative for direction / movement to somewhere:
in den Park = into the park

In this sentence, we’re talking about where we play (location), not movement into the park, so dative is used: im Park.

Why are Samstag, Park, Freundschaftsspiel, and Nachbarn capitalized?

In German, all nouns are capitalized, not just proper names.

Here, all these words are nouns:

Samstag – a day (noun)
Park – a place (noun)
Freundschaftsspiel – a thing, a match (noun)
Nachbarn – a person (noun, here in a declined form)

So they are written with a capital first letter, following the standard rule for German nouns.

Why is the present tense (spielen) used for a future event? Shouldn’t it be werden spielen?

German very often uses the present tense to talk about the near future, especially when the time is clear from context:

Am Samstag spielen wir … = We are playing / We’ll play on Saturday.

Using werden is possible but less common in casual speech:

Am Samstag werden wir im Park ein Freundschaftsspiel spielen.

The present tense with a time expression (like am Samstag) is the most natural here and corresponds well to English “We’re playing on Saturday”.