Learn Hardcore German: Wir sitzen auf dem Platz und trinken Wasser.

Wir sind auf dem Platz is not wrong, but it’s more neutral: We are on the square/field (there), without saying whether we are standing, sitting, walking, etc.
Wir sitzen auf dem Platz is more specific: we are sitting there.

In English we say “are sitting” and “are drinking.” Why is German just sitzen and trinken, not something like a progressive form?

German does not have a special “-ing” progressive tense like English.
The simple present in German covers both:

Wir sitzen auf dem Platz und trinken Wasser.
= We sit on the square and drink water.
= We are sitting on the square and drinking water.

Context tells you whether it’s a general habit or something happening right now. In this sentence, it’s naturally understood as happening now, just like an English progressive.

Why is there dem Platz with an article, but Wasser has no article?

Two different reasons:

Platz is a specific, countable thing.
- auf dem Platz = on the square/seat/field (a specific one)
- You need an article to show definiteness and case: dem = dative, masculine.
Wasser is a mass (uncountable) noun used in a general, indefinite sense.
- Wir … trinken Wasser. = We are drinking (some) water.
- With substances (water, milk, beer, coffee, etc.), German often drops the article when it means “some, not specified.”

You could use articles in other contexts:

Wir trinken das Wasser. = We are drinking the water (a specific water already known).
Wir trinken ein Wasser. (colloquial, especially in restaurants)
= We’re having a water (one serving/bottle/glass of water).

What exactly does Platz mean here? “Square,” “seat,” or something else?

Platz is quite flexible in German. It can mean:

Public square / plaza
- Wir sitzen auf dem Platz. = We’re sitting on the town square.
Seat / place to sit
- Dein Platz ist hier. = Your seat/place is here.
- In some contexts, auf dem Platz sitzen could be understood as sitting in your seat/spot.
Sports field / pitch / court
- Der Fußballplatz = the football field
- Wir sitzen auf dem Platz (in a sports context) could mean on/at the pitch or field.

Without more context, Platz is usually understood as a square or an open space.

Why is it wir sitzen and then (wir) trinken without repeating wir?

German allows you to omit the subject in the second clause when it is clearly the same as in the first clause, especially with und:

Wir sitzen auf dem Platz und trinken Wasser.

This is like English:

“We are sitting on the square and (we) are drinking water.”

You can say Wir sitzen auf dem Platz und wir trinken Wasser, but it sounds heavier and is usually only done for emphasis or clarity. The shorter version is more natural.

Why is sitzen conjugated as wir sitzen and not something like wir sitz(en) or wir sitzten?

The infinitive is sitzen. The present-tense conjugation is:

ich sitze
du sitzt
er/sie/es sitzt
wir sitzen
ihr sitzt
sie/Sie sitzen

Patterns to notice:

wir and sie/Sie usually keep the infinitive form (-en ending).
Only ich, du, er/sie/es, and ihr change the ending more noticeably.

So wir sitzen follows the regular pattern: stem sitz- + -en for wir.

What case is Wasser in, and how can I tell if it’s accusative?

In this sentence, Wasser is accusative because it’s the direct object of the verb trinken:

Who is doing something? → wir (subject, nominative)
What are they drinking? → Wasser (direct object, accusative)

Neuter nouns like das Wasser look the same in nominative and accusative (without article you can’t see a change), so you rely on the role in the sentence:

Das Wasser ist kalt.
→ Das Wasser is the subject (nominative).
Wir trinken das Wasser.
→ das Wasser is the direct object (accusative).

In Wir trinken Wasser, the function (what is being drunk) tells you it’s accusative.

Why is there no comma before und in this sentence?

In modern German, you usually do not put a comma before und when it simply joins:

two verbs with the same subject
→ Wir sitzen … und trinken …
or two similar parts of a sentence (like in English: “We sit and drink.”)

You would use a comma with und if it joins two independent clauses that each have their own subject and verb, especially if the clauses are long:

Wir sitzen auf dem Platz, und die Kinder spielen auf der Wiese.
(Two full clauses: we sit… / the children play…)

Could we say Wir sitzen am Platz instead of auf dem Platz? What’s the difference between am and auf dem?

Am is a contraction of an dem (“at the / on the”, using an + dative).
Auf dem is auf + dative (“on the”).

The nuance:

auf dem Platz
→ literally “on the square / on the field / on the seat”
→ emphasizes being on the surface or area.
an dem Platz / am Platz
→ more like “at the place/spot/square” (near or at it, not necessarily on top of it).

In many everyday contexts, auf dem Platz is the more idiomatic expression for sitting somewhere on a square, field, playground, etc.
Am Platz can work, but it more often suggests being at/near that location rather than physically on it.

Why are Platz and Wasser capitalized, but wir, sitzen, auf, und, trinken are not?

In German, all nouns are capitalized, regardless of their position in the sentence:

Platz (noun) → capitalized
Wasser (noun) → capitalized

Verbs, pronouns, conjunctions, and prepositions are normally not capitalized, unless they are the first word of a sentence or part of a proper name:

wir (pronoun) → lowercase
sitzen, trinken (verbs) → lowercase
auf, und (preposition, conjunction) → lowercase

So capitalization here is simply following the standard rule: nouns uppercase, everything else lowercase (except at the start of the sentence).