Learn Hardcore Indonesian: Matahari terbit di timur.

In modern Indonesian matahari is written as one word.
It’s capitalized here only because it starts the sentence, not because it’s treated as a proper noun.

What kind of verb is terbit and what does the prefix ter- do?

terbit is an intransitive verb meaning “to rise” (of the sun) or “to appear.”
The prefix ter- often marks a spontaneous, accidental, or resultant state. Here it forms the verb “to rise.”

Why is there no article like the before sun or east?

Indonesian does not use definite or indefinite articles. Context alone tells you if something is specific, so you simply say matahari or timur without the.

What is the function of di in di timur?

di is a preposition indicating location (“in/at/on”).
di timur = “in the east.”
If you wanted to express movement toward the east, you’d use ke timur (“to the east”).

Can I say Matahari terbit dari timur instead?

You can, but it’s less idiomatic. dari timur means “from the east,” shifting the nuance slightly. Native speakers usually say di timur when referring to where the sun rises.

How do I say “The sun rises in the east every day”?

Add a time adverb:

Matahari terbit di timur setiap hari.
Or reorder if you prefer:
Setiap hari matahari terbit di timur.

If I want to say “The sun rose in the east yesterday,” how would I do that?

Since terbit doesn’t change form for past tense, you add a time word:

Kemarin matahari terbit di timur.