Learn Hardcore Indonesian: Meja di ruang tamu dibersihkan dulu sebelum rapat dimulai. - The table in the living room is cleaned first before the meeting starts.

Dibersihkan is the passive form (di- + bersih + -kan) and focuses on the thing being cleaned (meja), not on who does the cleaning.
If you used membersihkan (active), you’d normally need an explicit doer/subject, e.g. (Saya) membersihkan meja… = “I clean the table…”

Does this sentence sound like an instruction (“Clean the table…”) or a statement (“The table is cleaned…”)?

It can be understood as either depending on context, because Indonesian often drops the agent:

As a procedural instruction (common in meetings/work): “The table should be cleaned first…”
As a neutral statement: “The table is cleaned first…”

If you want a clear command, you could use:

Bersihkan dulu meja di ruang tamu… (more direct/imperative)

Where is the “doer” of the action? Who cleans the table?

It’s intentionally not mentioned. Indonesian passive sentences often omit the agent when it’s obvious, unimportant, or you want to sound more polite/impersonal.
You can add the agent with oleh:

Meja di ruang tamu dibersihkan dulu oleh panitia… = “The table … is cleaned first by the committee…”

What exactly does dulu mean here?

Dulu here means “first / beforehand” (sequence), not “in the past.”
So dibersihkan dulu sebelum… = “cleaned first before…”

For a more formal version you can say:

dibersihkan terlebih dahulu sebelum…

Why is dulu placed after dibersihkan?

In Indonesian, adverbs like dulu commonly come after the verb they modify:

dibersihkan dulu = “cleaned first”

You could move it for emphasis, but this is the most natural placement in everyday Indonesian.

What is the function of di ruang tamu? Is it describing the table or the cleaning?

It primarily identifies which table: “the table in the living room.”
Structurally it attaches to meja as a location phrase:

Meja [di ruang tamu] = “the table [in the living room]”

Why is di sometimes separate (di ruang tamu) and sometimes attached (dibersihkan, dimulai)?

They are two different di’s:

di + place (separate) = preposition meaning “in/at” → di ruang tamu
di- + verb (attached) = prefix marking passive voice → di-bersih-kan, di-mulai

Spelling is a big clue: preposition di is written separately; prefix di- is written together.

What does dibersihkan literally mean, and why is there -kan?

dibersihkan comes from:

bersih = “clean”
-kan often makes it causative/transitive: “make (something) clean” → “clean (something)”
di- makes it passive: “be cleaned”

So dibersihkan = “is cleaned / gets cleaned.”

Why does the second clause use rapat dimulai instead of rapat mulai?

Both can work, with slightly different feel:

rapat mulai = “the meeting starts” (more direct/intransitive)
rapat dimulai = “the meeting is started / is begun” (passive/impersonal; sounds a bit more formal/administrative)

In schedules/announcements, dimulai is very common.

Is sebelum used like “before” in English? Does it need any special grammar?

Sebelum works much like English “before”, introducing a time clause:

… sebelum rapat dimulai = “… before the meeting begins/is begun”

Indonesian doesn’t change verb forms for tense the way English does, so you don’t need something like “will” or “had.”

Why isn’t there an equivalent of “the” (like “the table” / “the meeting”)?

Indonesian doesn’t have articles like the/a. Definiteness is usually inferred from context.
If you want to make it more specific, you can add:

meja itu = “that/the table”
rapat ini = “this/the meeting”
mejanya can mean “the table (of the situation/house)” depending on context

Could I say Meja di ruang tamu dibersihkan sebelum rapat dimulai dulu?

That sounds awkward because dulu naturally modifies the first action (dibersihkan) rather than the time clause.
Best options:

Meja di ruang tamu dibersihkan dulu sebelum rapat dimulai. (natural)
Sebelum rapat dimulai, meja di ruang tamu dibersihkan dulu. (same meaning, different emphasis)