Learn Hardcore Malay: Masalah itu sudah selesai. - That problem is already solved.

Itu is a demonstrative that usually means "that," and it also works like a definite article "the" when the referent is known. It follows the noun: masalah itu = "that/the problem" (a specific, identifiable problem). Without itu, masalah is more general or newly introduced.

Could I use ini instead of itu?

Yes. Ini means "this" (near/immediate/newly introduced). Masalah ini sudah selesai = "This problem is already solved." Use itu for something previously mentioned, known, or not immediate.

Do I need both sudah and selesai? What’s the nuance of Masalah itu selesai vs Masalah itu sudah selesai?

Masalah itu selesai states a present state: "The problem is resolved/finished."
Masalah itu sudah selesai highlights completion relative to a prior point or expectation: "The problem has already been resolved." Both are correct; sudah adds the "already/completed" nuance.

What’s the difference between sudah, telah, dah, and udah?

sudah: neutral, very common.
telah: more formal/literary (news, official text).
dah: colloquial Malaysian contraction of sudah.
udah: colloquial Indonesian contraction of sudah. All can fit: Masalah itu telah selesai (formal), Masalah itu dah selesai (informal MY), Masalah itu udah selesai (informal ID).

Why is there no word for "is/has been"?

Malay usually omits a copula before adjectives/stative verbs and uses aspect markers instead of tense. Sudah provides the completion meaning that English expresses with "has been." Hence Masalah itu sudah selesai ≈ "The problem has been solved."

How do I say "not yet" vs "not" with this sentence?

"Not yet": Masalah itu belum selesai. (belum = not yet, implying it may be solved later.)
Plain negation: Masalah itu tidak selesai. (States it is not solved; can sound more final or factual, depending on context.)

Can I move sudah elsewhere? Is Masalah itu selesai sudah okay?

Neutral word order is subject + aspect + predicate: Masalah itu sudah selesai. Final ...selesai sudah occurs in some dialects/poetic styles; stick to sudah selesai for standard speech. You can also say Itu sudah selesai ("That is already finished") when itu stands alone as "that."

How do I include who solved it?

Use transitive forms:

Passive, no agent: Masalah itu sudah diselesaikan.
Passive with agent: Masalah itu sudah diselesaikan oleh pasukan IT.
Active: Pasukan IT sudah menyelesaikan masalah itu. The original sudah selesai focuses on the result, not the agent.

How do I turn it into a question: "Has the problem been solved?"

By intonation or question particles, depending on register:

Informal (Malaysia): Masalah itu dah selesai ke?
Neutral: Masalah itu sudah selesai? (rising intonation)
Formal: Adakah masalah itu telah selesai?
Indonesian informal: Masalah itu udah selesai?

Is sudah selesai redundant?

No. Selesai = finished/resolved (state). Sudah = already (completion). Together they make a very common, idiomatic pairing, like "already finished" in English.

Could I drop itu? Difference between Masalah sudah selesai and Masalah itu sudah selesai?

Masalah sudah selesai is less specific; it can mean "the problem is solved" in general or "problems are solved" (context decides).
Masalah itu sudah selesai points to a specific known problem.

What’s the difference between selesai, siap, and habis?

selesai: finished/resolved (best for issues/problems, tasks).
siap: ready/done/prepared (an item/task is ready for use). Kerja itu sudah siap.
habis: finished/run out/used up (quantities, time). Duit sudah habis. For problems, use selesai.

Are there more formal alternatives to itu?

Yes: tersebut ("the aforementioned") and berkenaan ("in question"):

Masalah tersebut telah selesai.
Masalah berkenaan telah selesai.

Does this sentence work in Indonesian too? Any differences?

Yes, it’s equally natural in Indonesian: Masalah itu sudah selesai. Register differences: Indonesian colloquial prefers udah; Malaysian colloquial uses dah. Formal telah is fine in both.