Learn Hardcore Indonesian: Walau saya lelah, saya tetap belajar di perpustakaan. - Although I am tired, I still study in the library.

walau – a bit shorter, very common in speech and writing.
walaupun – slightly more formal or explicit, but still very common.
meski / meskipun – also common; many speakers feel meskipun and walaupun sound a bit more formal or literary than walau.

Can the order of the two clauses be reversed?

Yes. You can say:

Walau saya lelah, saya tetap belajar di perpustakaan.
Saya tetap belajar di perpustakaan walau saya lelah.

Both are natural. Putting the walau-clause first slightly emphasizes the contrast:

First version: stronger feeling of even though.
Second version: feels more like I still study at the library, even though I am tired (focus on the studying first).

Why is there no word like am in saya lelah?

Indonesian normally does not use a separate verb to be before adjectives.

saya lelah literally is I tired, but it means I am tired.
dia lapar = he/she is hungry.
mereka sibuk = they are busy.

So lelah is just an adjective, and saya is the subject. You do not add anything like am or is in this structure.

What exactly does tetap add here?

Tetap carries the idea of still / nonetheless / despite that, continuing as usual.

In this sentence:

Saya belajar di perpustakaan = I study at the library.
Saya tetap belajar di perpustakaan = I still study at the library, I keep on or continue to study there in spite of something.

Combined with walau saya lelah, tetap highlights the contrast:

Tiredness would normally stop or reduce studying, but you continue anyway.

What is the difference between tetap, masih, and terus?

All three can be translated as still / continue, but they are used differently:

tetap – remain / stay / nonetheless. Focus on not changing despite something.
- Walau hujan, kami tetap pergi.
  Even though it is raining, we still go.
masih – still (not yet finished, not yet changed). Often used with states that continue.
- Saya masih lelah.
  I am still tired.
terus – keep doing, go on, continuously. Focus on ongoing action.
- Dia terus belajar sampai malam.
  He keeps studying until night.

In your sentence, tetap is best because it shows you continue as planned despite being tired.

Are lelah and capek the same? Which sounds more natural?

They are very close in meaning:

lelah – tired, fatigued; sounds a bit more neutral/formal or written.
capek / capai – tired, worn out; more colloquial, very common in speech.

More natural choice depends on context:

In everyday casual conversation: Saya capek, tapi saya tetap belajar. is very common.
In writing, textbooks, or slightly formal speech: Saya lelah, tapi saya tetap belajar.

Both are correct; lelah is just a little more neutral.

Could I drop the second saya and just say Walau saya lelah, tetap belajar di perpustakaan?

Yes, in informal spoken Indonesian, dropping the repeated subject is common when it is clear from context. For example:

Walau saya lelah, tetap belajar di perpustakaan.

A more complete and slightly more standard version is:

Walau saya lelah, saya tetap belajar di perpustakaan.

In writing, especially for learners or in formal contexts, keeping the second saya is safer and clearer.

Is walau considered formal, neutral, or informal?

Walau is generally neutral:

It is perfectly fine in conversation.
It appears in newspapers, blogs, and many kinds of written text.

If you want to sound extra formal, for example in official writing, walaupun or meskipun might be preferred, but walau is not incorrect there. The difference is more about style than strict grammar.

Why do we use di in di perpustakaan, and not ke perpustakaan?

Because we are talking about the location of the studying, not the direction of movement.

di = at / in (location).
- Saya belajar di perpustakaan.
  I study in/at the library.
ke = to / toward (movement).
- Saya pergi ke perpustakaan.
  I go to the library.

In your sentence, the action is belajar (study) happening at a place, so di is correct.

Can I say di dalam perpustakaan instead of di perpustakaan?

Yes:

Saya tetap belajar di perpustakaan.
Saya tetap belajar di dalam perpustakaan.

Di dalam perpustakaan makes it slightly more explicit that it is inside the library building, but usually di perpustakaan already implies that. In most contexts they are interchangeable; di perpustakaan is shorter and more common.

Can I omit walau and say Saya lelah, tapi saya tetap belajar di perpustakaan?

Yes. That is a very natural alternative:

Saya lelah, tapi saya tetap belajar di perpustakaan.
I am tired, but I still study at the library.

Difference:

walau introduces a subordinate clause (although…).
tapi is a coordinating conjunction (but) connecting two equal clauses.

Both express contrast; walau feels slightly more like written style or structured contrast, while tapi is extremely common in speech.

Can I replace saya with aku here?

Grammatically, yes:

Walau aku lelah, aku tetap belajar di perpustakaan.

The main difference is formality and distance:

saya – more formal/polite or neutral; safe with strangers, teachers, older people, in writing.
aku – more intimate/informal; used with friends, family, people close to you.

Both are correct; choose based on who you are talking to and the tone you want.

Is the comma after lelah necessary? How is it pronounced in speech?

In writing, the comma is standard:

Walau saya lelah, saya tetap belajar di perpustakaan.

It separates the walau-clause from the main clause.

In speech, this comma corresponds to a short pause after lelah:

Walau saya lelah [short pause] saya tetap belajar di perpustakaan.

The pause helps listeners process the contrast. You can also slightly raise your intonation on lelah, then continue with a normal or slightly falling intonation on saya tetap belajar di perpustakaan.