Learn Hardcore Indonesian: Papan pengumuman di tengah sekolah ditempeli poster baru. - The bulletin board in the middle of the school has a new poster stuck on it.

papan = board, plank
pengumuman = announcement(s), notice(s)
Together, papan pengumuman is a common compound meaning a notice board/bulletin board. It’s a normal, fixed-sounding collocation in Indonesian.

Does di tengah sekolah describe the board or the action? In other words, is it “the notice board in the middle of the school” or “was pasted in the middle of the school”?

Here it most naturally attaches to the noun phrase that precedes it: papan pengumuman [di tengah sekolah], i.e., “the notice board in the middle of the school.”
If you wanted it to modify the action (where the pasting happened), you could move it later: Papan pengumuman itu ditempeli poster baru di tengah sekolah.

How is ditempeli formed, and what nuance does it carry?

Root: tempel (stick/paste)
Passive prefix: di-
Suffix: -i (often marks the target/location/recipient)
So di-tempel-i means “to be pasted/stuck on (as the target).” The subject is the surface/location affected (here, the board). The -i form can also suggest the surface may have multiple items attached or is treated as a location being acted on.

What’s the difference between ditempeli, ditempel, and ditempelkan?

ditempeli: the subject is the location/target. Example: Papan itu ditempeli poster.
ditempel: plain passive “to be pasted.” The natural subject is the thing pasted. Example: Poster itu ditempel di papan. (Here, the poster is the subject, not the board.)
ditempelkan: causative passive, focusing on causing something to be attached somewhere. Example: Poster itu ditempelkan di papan.
Your original sentence uses ditempeli because the board is the affected surface.

Could I add dengan after ditempeli (e.g., ditempeli dengan poster baru)?

Yes. Both ditempeli poster baru and ditempeli dengan poster baru are acceptable. Adding dengan makes the “means/material” relationship explicit but isn’t required.

Why is there no agent (like “by the students”)? How do I add one?

Indonesian passives often omit the agent if it’s unknown or unimportant. To add it, use oleh:

Papan pengumuman di tengah sekolah ditempeli poster baru oleh para siswa.
Or switch to an active sentence:
Para siswa menempelkan poster baru pada papan pengumuman di tengah sekolah.

Is poster baru singular or plural? How do I make that clear?

By default it’s number-neutral. Clarify with quantifiers/markers:

Singular: sebuah poster baru, satu poster baru
Plural (general): beberapa poster baru
Plural (emphatic): poster-poster baru
Many: banyak poster baru
Note: ditempeli can suggest a surface with items on it, but you still need quantifiers if number matters.

Do I need yang (e.g., poster yang baru)?

Not here. A simple adjective follows the noun: poster baru = “new poster.”
yang is used before longer descriptors or for emphasis/contrast: poster yang baru can mean “the new one (as opposed to the old one).”

How do I express tense/aspect with this sentence?

Indonesian verbs don’t inflect for tense. Use particles/adverbs:

Completed: sudah/telah — Papan ... sudah ditempeli poster baru.
Ongoing: sedang — Papan ... sedang ditempeli poster baru.
Future/intended: akan/akan segera — Papan ... akan ditempeli poster baru.
Just now: baru saja — Papan ... baru saja ditempeli poster baru.

Should di tengah be written as two words or one?

Two words. di as a preposition (at/in/on) is written separately from the noun: di tengah.
One-word di- is a prefix only in passive verbs (e.g., ditempeli).

Is di tengah sekolah the best way to say “in the middle of the school grounds”? Any alternatives?

di tengah sekolah is fine but a bit general. To be clearer:

di tengah halaman sekolah (in the middle of the school yard)
di tengah kompleks sekolah (in the middle of the school complex)
Intensified: di tengah-tengah sekolah (right in the middle)

What would be natural informal variants I might hear?

Colloquially:

Papan pengumuman di tengah sekolah ditempelin poster baru. (informal passive with -in)
Posternya nempel di papan pengumuman. (intransitive nempel “is stuck”)
These are common in casual speech but avoid them in formal writing.

Can I add yang to highlight which board I mean?

Yes, to single out that specific board:
Papan pengumuman yang di tengah sekolah ditempeli poster baru.
This stresses “the one that is in the middle of the school.”

Could baru mean “just now” here?

In poster baru, baru is an adjective meaning “new.”
As an adverb meaning “just (now)”, baru precedes a verb/clause: Papan itu baru ditempeli (tadi). = “The board was just pasted (a moment ago).”