Learn Hardcore Indonesian: Kami pun makan ikan bakar di warung di ujung pantai. - We also eat grilled fish at the stall at the end of the beach.

pun is a particle that links this sentence to the previous context. It typically means also/as well, and in narratives it can feel like so/then. It adds a light emphasis or continuity. Without pun, the sentence is still correct; it just loses that additive/transition nuance.

Neutral alternative: Kami juga makan...
Slightly formal/story-like: Kami pun makan...
Stronger even: Bahkan kami makan... (different emphasis)

Can I just replace pun with juga? Any difference in tone or position?

Yes. Kami juga makan... is the most neutral way to say we also ate.... Differences:

Tone: pun sounds a bit more literary or narrative; juga is everyday.
Position: pun follows the word it emphasizes (here the subject: Kami pun). juga usually goes before the verb or at the end of the clause: Kami juga makan...; Kami makan juga is possible but less common.

Where else can pun go, and what changes if I move it?

pun follows and emphasizes the word directly before it.

Kami pun makan... emphasizes that it was we (not others) who also/then ate.
Makan pun kami... is used for emphasis like even eating (we) didn’t have time for; typically in negative or contrastive contexts: Makan pun tidak sempat.
Kami makan pun... is generally not natural.

Why is di repeated in di warung di ujung pantai? Can I drop one di?

You have two nested location phrases: at a stall, and that stall is at the end of the beach. Indonesian normally repeats di for each location:

Natural: di warung di ujung pantai
Also fine (a bit more explicit/formal): di warung yang (berada) di ujung pantai
Less natural if you drop the second di: di warung ujung pantai (may sound like a named place)

Do I need yang as in di warung yang di ujung pantai?

No. Yang is optional here. Adding yang (berada) can make the modifying relationship explicit or a bit more formal: di warung yang berada di ujung pantai. Without yang, everyday Indonesian stacks the di-phrases just fine: di warung di ujung pantai.

What exactly is a warung?

A warung is a small, usually family-run stall or simple eatery that sells inexpensive food or groceries. Rough guide:

warung/warung makan: small, simple, informal
rumah makan: casual sit-down eatery
restoran: restaurant, more formal
warteg: a type of warung serving Javanese/home-style dishes

Why kami and not kita?

Both mean we, but:

kami excludes the listener (we, not including you).
kita includes the listener (we, including you). So Kami pun... implies the speaker’s group did it, but not the person being addressed.

Why is it just makan and not memakan?

For eating food, plain makan with a direct object is the default: makan ikan bakar. Memakan is more formal/literary or used in special senses:

Literal but formal: memakan ikan (sounds stiff).
Idiomatic: memakan waktu (to take time), memakan korban (to claim victims).
Animals preying: ular itu memakan tikus (acceptable).

Is ikan bakar an adjective-noun phrase? How is it different from membakar ikan or ikan yang dibakar?

ikan bakar = noun + adjective/participial modifier: the dish/style grilled fish.
membakar ikan = verb phrase: to grill fish.
ikan yang dibakar = relative clause: fish that is grilled (more explicit/formal). In Indonesian, modifiers follow the noun, so ikan bakar is the normal word order.

Does ikan bakar mean one fish or several? How do I show quantity?

By default, number is unspecified. To be specific, use classifiers or measures:

One whole fish: seekor ikan bakar
A portion/serving: seporsi ikan bakar
A plate: sepiring ikan bakar
A piece: sepotong ikan bakar
Plural (some): ikan-ikan bakar or add a number: dua porsi ikan bakar

How do I mark past, present, or future in this sentence?

Indonesian verbs don’t inflect for tense. Use time/aspect words:

Past/completed: Kami sudah makan..., Kami tadi makan..., Kami baru saja makan...
Ongoing: Kami sedang makan..., Kami lagi makan... (informal)
Future/intent: Kami akan makan..., Nanti kami makan...

What’s the nuance of di ujung pantai? How is ujung different from tepi/pinggir/akhir?

ujung = the far end/tip of something with length; ujung pantai suggests one end of the stretch of beach.
tepi/pinggir = edge/side; tepi pantai/pinggir pantai means the shoreline.
akhir is more abstract (the end of a process/period) and isn’t used for physical tips like a beach.

Should di be written together or separately? I’ve seen both.

Two different things:

di as a preposition (location) is separate: di warung, di ujung.
di- as a passive prefix attaches to verbs: dimakan, dibakar. So write di warung (separate) but dimakan (together). Avoid di makan for the passive.

Is pun always separate? I’ve also seen forms like walaupun.

The particle pun is written as a separate word when it stands alone, as here: Kami pun.... In some fixed words/expressions it fuses, for example: walaupun, meskipun, sekalipun, biarpun, adapun, bagaimanapun. With indefinites like apa pun/siapa pun, many modern style guides write them as two words.

Could I say the same thing without pun? Does it change the meaning?

Yes: Kami makan ikan bakar di warung di ujung pantai is perfectly natural. Removing pun keeps the core meaning but removes the sense of also/so/then that ties it to prior context. If you want a neutral also, use juga.