Learn Hardcore Indonesian: Dia belajar bermain gitar agar bisa menyanyi lagu sendiri. - He/She learns to play the guitar so that he/she can sing his/her own songs.

agar is a conjunction meaning “so that” or “in order to.” It introduces a purpose clause, linking the action of the main clause (learning guitar) to the intended outcome (being able to sing one’s own songs).

Can agar be replaced by other words like supaya or untuk?

supaya is a direct synonym of agar and can be used interchangeably:
Dia belajar bermain gitar supaya bisa menyanyi lagu sendiri.
untuk also indicates purpose but usually follows the infinitive directly and often drops bisa:
Dia belajar bermain gitar untuk menyanyi lagu sendiri.
This version focuses on the goal (“to sing”) rather than on acquiring the ability (“can sing”).

Why is it belajar bermain gitar instead of just belajar gitar or belajar main gitar?

belajar gitar (“learn guitar”) is perfectly common in everyday speech.
belajar bermain gitar (“learn to play guitar”) explicitly uses bermain to clarify the action “to play.”
belajar main gitar is the informal spoken form (dropping the ber- in bermain).
All three express essentially the same idea, with slight differences in formality and precision.

What role does bisa play in agar bisa menyanyi? Could it be omitted?

bisa means “can” or “to be able to.” Including it stresses that the learner wants to gain the ability to sing. If you omit bisa, you still express purpose:
Dia belajar bermain gitar agar menyanyi lagu sendiri.
Here, the focus shifts slightly to “in order to sing” rather than “in order to be able to sing.”

What does sendiri mean in lagu sendiri? How does it affect the meaning?

In lagu sendiri, sendiri means “own.” So lagu sendiri = “one’s own song(s).”
You could also say:

lagu dia sendiri (wordier)
lagunya sendiri (adds the possessive suffix -nya)
but lagu sendiri is more concise and idiomatic.

What gender does dia indicate in this context?

dia is a gender-neutral third-person pronoun in Indonesian, meaning “he” or “she.” There is no separate word for “he” vs. “she” – context tells you which one.

Why is the purpose clause placed at the end? Can it appear at the beginning?

Typically, Indonesian puts subordinate clauses (like purpose clauses) after the main clause:
Dia belajar bermain gitar agar bisa menyanyi lagu sendiri.
However, you can front it for emphasis or a formal tone:
Agar bisa menyanyi lagu sendiri, dia belajar bermain gitar.
Both orders are grammatically correct.

Why aren’t there any articles like “the” or “a” before gitar or lagu?

Indonesian does not use definite or indefinite articles (such as “the” or “a”). Nouns stand alone, and context or additional words (quantifiers, demonstratives) clarify specificity.