Learn Hardcore Hungarian: A könyvtárban szabad vizet inni. - In the library it is allowed to drink water.

szabad + infinitive means something is permitted/allowed.
lehet + infinitive means something is possible; in practice it often also implies permission, but it can be ambiguous (possible vs permitted).
ingyen/ingyenes means free of charge. So szabad vizet inni is about permission, not price. For “free water,” you’d say ingyen (van) víz or ingyenes a víz.

Why is there no explicit subject (like “you/people”) and no form of van?

Hungarian often uses impersonal, subjectless sentences for general rules. Here, szabad is the predicate, and in the present tense the copula van is omitted in 3rd person. So the present is simply A könyvtárban szabad vizet inni.

Past/future require the copula: A könyvtárban szabad volt/lesz vizet inni.

Why is the verb inni (infinitive) and not a conjugated form like iszom/iszik?

After modal-like words and predicates such as szabad, lehet, kell, tilos, Hungarian uses the infinitive (-ni form): inni. You should not conjugate the verb here. So not: ✗ A könyvtárban szabad iszom/iszik vizet; ✓ … szabad vizet inni.

Why is it vizet and not víz or a vizet?

vizet is the accusative singular of víz (object form), marked with -t. It corresponds to English “water” as a mass object (“drink water/some water”).
Bare víz would be the nominative (subject) form.
a vizet (definite accusative) would mean “the water” (some specific water already mentioned), which isn’t the generic meaning here.

How is vizet formed from víz? It looks irregular.

The noun víz forms its accusative as vizet: the long í shortens to i, a linking vowel -e- appears, and the accusative -t is added. So: víz → vizet. Other case forms: vízben (in water), vízből (from water), vízzel (with water).

What does könyvtárban mean exactly, and why is it -ban and not -ben?

könyvtár = library; -ban/-ben is the inessive case “in, inside.” So könyvtárban = “in the library.”
Vowel harmony chooses -ban (back-vowel variant) because könyvtár contains the back vowel á. Rule of thumb: if a word has any back vowels (a, á, o, ó, u, ú), use the back suffix; otherwise use the front one (-ben).

Why is the article a used (a könyvtárban), and could it be az?

Hungarian uses a before consonant-initial words and az before vowel-initial words. könyvtárban starts with a consonant sound (k), so it’s a könyvtárban, not az könyvtárban.

Do I need the article at all? What changes if I drop it?

A könyvtárban… generally points to a specific library (the one we’re talking about or “the library” as the local institution).
Könyvtárban… without the article is more generic, roughly “In libraries (as a rule)…” You can also make it explicitly plural: A könyvtárakban… = “In libraries.”

Can I move the words around? What are natural alternatives and what do they emphasize?

Yes, Hungarian word order is flexible and used for emphasis.

Neutral options: A könyvtárban szabad vizet inni. / Szabad vizet inni a könyvtárban.
To emphasize the allowed thing, put it right before szabad: VIZET szabad inni a könyvtárban.
To emphasize the place, keep A könyvtárban before szabad: A könyvtárban szabad vizet inni.
These are all grammatical; the main difference is what you want to highlight.

Can I say inni vizet instead of vizet inni?

Both exist, but with infinitives the neutral, most typical order is object + infinitive: vizet inni. The order inni vizet can appear in certain emphatic or stylistic contexts, but here vizet inni is the plain, natural choice.

How do I say it’s not allowed or it’s forbidden?

Not allowed: Nem szabad vizet inni a könyvtárban. (= You mustn’t/You’re not allowed to drink water in the library.)
Forbidden (stronger): Tilos vizet inni a könyvtárban.

Can I use lehet instead of szabad? Does it change the meaning?

You can say A könyvtárban lehet vizet inni. In many contexts it will be understood as permission. However, lehet also means “it’s possible,” so it might be interpreted as “it’s feasible/there’s a chance to” (e.g., there’s water available). Szabad unambiguously expresses permission, so it’s the safest choice for rules.

How do I specify who is allowed? For example, “Students may drink water in the library.”

Use the dative for the allowed party:

A diákoknak szabad vizet inni a könyvtárban. (= Students are allowed to drink water in the library.) You can also front the dative for emphasis: A diákoknak szabad…

How do I add “only,” as in “Only water may be drunk in the library”?

Put csak before the focused element:

A könyvtárban csak vizet szabad inni. (= In the library, only water may be drunk.) If you mean only that place, not elsewhere: Csak a könyvtárban szabad vizet inni.

How do I ask this as a yes–no question?

Just use question intonation and a question mark:

Szabad vizet inni a könyvtárban?
Alternatively: Lehet vizet inni a könyvtárban?

What’s the difference between könyvtárban and könyvtárba?

könyvtárban = in(side) the library (location; static).
könyvtárba = into the library (direction; movement toward/into). So A könyvtárban szabad… is “In the library it’s allowed…”, not “Into the library…”

How do I put the sentence in the past or future?

Use the copula in past/future:

Past: A könyvtárban szabad volt vizet inni. (= It was allowed to drink water in the library.)
Future: A könyvtárban szabad lesz vizet inni.

Any quick pronunciation tips for tricky letters here?

ö in könyvtárban is like French “eu” in “peur.”
á is a long open “a.”
sz (in szabad) sounds like English “s”; note that Hungarian s (not present here) is “sh.”
ny is a single sound (like Spanish ñ). In könyvtárban, you hear ny followed by v across the word boundary from könyv (book) → könyvtár (library).