Learn Hardcore Indonesian: Rencana tim ditulis singkat agar semua orang paham. - The team plan is written briefly so that everyone understands.

Yes. ditulis is the passive form of menulis (“to write”). The prefix di- marks passive voice with the patient as subject. The agent (the writer) is omitted, which is common in Indonesian.

You can add the agent with oleh: Rencana tim ditulis singkat oleh manajer. (The team plan was written briefly by the manager.)
Or use the “short passive” (passive type 2): Rencana tim saya tulis singkat. (I wrote the team plan briefly.)

Can I rephrase it in active voice?

Yes:

Tim menulis rencana itu secara singkat agar semua orang paham. (The team wrote the plan briefly so everyone understands.)
With a specific agent: Manajer menulis rencana tim secara singkat agar semua orang paham.

Is "singkat" an adjective or an adverb here? Do I need "secara singkat"?

Here singkat functions adverbially (“briefly”), modifying ditulis. Indonesian often uses adjectives as adverbs of manner.

ditulis singkat and ditulis secara singkat both work; the latter is a bit more formal.
Position: put it after the verb for manner. Rencana tim singkat would mean “a brief team plan” (adjective modifying the noun), not “written briefly.”

Why not use "pendek" for “short”?

Pendek refers to physical/temporal length (short height, short duration). For conciseness in writing, use singkat or ringkas:

ditulis singkat/ringkas = written concisely.
pendek sounds off for text style.

What does "agar" mean here? How is it different from "supaya", "biar", or "untuk"?

agar = “so that / in order that”; slightly formal.
supaya ≈ agar, neutral–informal.
biar = informal colloquial.
untuk = “for/to,” but it needs a noun/gerund-like phrase: … untuk membuat semua orang paham. You can’t say untuk semua orang paham without a verb like membuat. Only agar/supaya/biar directly take a clause.

Can I put the "agar" clause at the beginning?

Yes: Agar semua orang paham, rencana tim ditulis singkat. Use a comma when the purpose clause comes first. When it comes second, a comma is usually omitted.

Does "paham" need an object or a preposition?

Not necessarily. paham can be intransitive: semua orang paham = “everyone understands.” If you specify what they understand, you can:

say it directly (common in speech): Saya paham rencana ini.
or add a preposition (more formal): Saya paham akan rencana ini / paham terhadap rencana ini. With the transitive memahami, you must include an object: Saya memahami rencana ini.

What’s the difference among "paham", "mengerti", and "memahami" (and the colloquial "ngerti")?

paham: intransitive or lightly transitive; neutral; also works as a predicate adjective.
mengerti: intransitive; standard; ngerti is informal.
memahami: transitive “to comprehend [something]” (needs an object). All fit this context; with memahami you’d include the object: agar semua orang memahami rencana itu.

Could I use "dipahami" instead of "paham"?

Yes, that makes the plan the grammatical subject:

Agar rencana tim dapat/bisa dipahami semua orang.
More formal with agent phrase: Agar rencana tim dapat dipahami oleh semua orang. Your original keeps people as the subject; these versions focus on the plan.

Is "semua orang" the same as "orang-orang" or "setiap orang"? Should I ever say "semua orang-orang"?

semua orang = everyone, all people.
orang-orang = people (plural, general).
setiap orang = each person, every individual. Don’t double-mark plurality: avoid semua orang-orang. Use either semua orang or orang-orang, not both.

There’s no article like “the” in "rencana tim". How do I show definiteness or possession?

Indonesian has no articles; context supplies definiteness. To make it explicit:

rencana tim itu/ini/tersebut = that/this/the said team plan.
rencana timnya can mean “the team’s plan” (definite) or “his/her team’s plan,” depending on context. rencana dari tim (“plan from the team”) is possible but heavier; rencana tim is usually best.

Should "di" in "ditulis" be written together or separated?

Together. di- is a verb prefix for the passive and attaches to the verb: ditulis, dibaca, dibuat. Write di separately only when it’s the preposition “at/in/on”: di rumah, di kantor.

What’s the difference between "ditulis" and "tertulis"?

ditulis = “is/was written” (action or manner): ditulis singkat.
tertulis = “written” as a state/attribute: peraturan tertulis (written rules), secara tertulis (in writing). You wouldn’t normally say rencana tim tertulis singkat.

Do I need "bisa" in "agar semua orang paham"?

Optional. agar semua orang paham is already fine. Adding bisa/dapat emphasizes ability/possibility: agar semua orang bisa paham ≈ “so that everyone can understand.”