Learn Hardcore Indonesian: Gerbang barat sekolah selalu terbuka di pagi hari. - The west gate of the school is always open in the morning.

Here barat sekolah functions as a single unit meaning “the west (side) of the school.” That entire unit then modifies gerbang. So the structure is:
gerbang + [barat sekolah]
and it literally means “the gate at the west side of the school,” i.e. the school’s west gate.

In Indonesian, a noun or noun phrase that specifies location often follows the main noun, forming sequences like this without additional particles.

Why is selalu placed before terbuka? Could it go elsewhere?

selalu means “always” and is an adverb. In Indonesian, adverbs of frequency (selalu, sering, kadang-kadang, etc.) typically go immediately before the verb or adjective they modify. Here terbuka (“be open”) is the main predicate, so you say selalu terbuka = “always open.”

You generally would not put selalu after terbuka (e.g. terbuka selalu) in standard word order for adverb placement—though colloquially you might hear more flexible ordering in fast speech.

What does the prefix ter- do to buka in terbuka? Why isn’t it just buka?

buka by itself can be a verb “to open (something)” or an adjective “open,” but it often implies an action someone does (e.g. dia buka pintu “he opens the door”).
Adding ter- turns it into a stative or inchoative form: “to be open” or “become open without an external agent.”

So terbuka focuses on the state (“is open”), which is perfect for saying the gate remains open. If you said selalu buka, native speakers might understand you, but it sounds more like shorthand or colloquial; selalu terbuka is more standard for the stative sense.

Why use di pagi hari for “in the morning”? Can I say just pagi or use pada instead of di?

di is the preposition for general time expressions (like “in/at”).
pagi hari = “morning period.” You often see both words together in more formal or neutral contexts.
In casual speech, people often just say pagi without hari:
• Gerbang barat sekolah selalu terbuka pagi.

You can also use pada pagi hari if you want a more formal tone:
• Gerbang barat sekolah selalu terbuka pada pagi hari.

There’s no word for “the” or “a”—is that normal in Indonesian?

Yes. Indonesian does not have articles like the or a. Definiteness and indefiniteness are usually inferred from context. So gerbang barat sekolah can mean “the west gate of the school” or “a west gate of the school,” depending on context.

I don’t see any verb like “is.” Where is the “to be” in this sentence?

Indonesian often omits a separate copula (the equivalent of “to be”) in present‐tense descriptive sentences. You simply put the subject and then the predicate adjective or stative verb.
Subject + Predicate Adjective/Verb
Gerbang barat sekolah + selalu terbuka di pagi hari
The linking idea “is” is implied.