Learn Hardcore Indonesian: Setelah polisi datang dan memeriksa, kami tidak curiga lagi. - After the police came and checked, we were no longer suspicious.

Setelah means after. It introduces a time clause: Setelah polisi datang dan memeriksa = After the police came and examined/checked.
Structurally, you have:

Setelah + clause, main clause
→ Setelah polisi datang dan memeriksa, kami tidak curiga lagi.

You could switch the order in Indonesian: Kami tidak curiga lagi setelah polisi datang dan memeriksa. The meaning is the same.

Why is there no past tense marker like came / examined in Indonesian?

Indonesian verbs usually do not change form for past, present, or future. The time is understood from context and time words.
In this sentence, setelah (after) already implies that the actions are in the past relative to kami tidak curiga lagi, so datang and memeriksa stay in their basic form.
So datang can mean come, came, or will come, depending on context.

Who is doing datang and memeriksa? Is the subject repeated?

The subject of both verbs is the same: polisi.
Indonesian often mentions the subject once, then uses multiple verbs after it:

polisi datang dan memeriksa
= the police came and examined/checked

You don’t need to repeat polisi before memeriksa.

Why is there no object after memeriksa? What is being examined?

In Indonesian, the object can be omitted when it is obvious from context or not important.
Here, memeriksa could mean checked the situation, inspected the place, questioned us, etc. The exact object is left implicit because the key point is simply that the police carried out some kind of examination.
If you want to be explicit, you could say:

Setelah polisi datang dan memeriksa kami, kami tidak curiga lagi.
(After the police came and examined us, we were not suspicious anymore.)

Is polisi singular or plural here? Does it mean the police as an institution or several officers?

Polisi can mean:

the police as an institution, or
one or more police officers

Indonesian often does not mark singular/plural. Context decides.
If you want to emphasize plural people, you can say para polisi (the police officers), but in this sentence polisi is natural and usually understood like English the police.

Why is kami used instead of kita?

Both kami and kita mean we, but:

kami = we (not including the person you are talking to)
kita = we (including the person you are talking to)

In this sentence, kami suggests that the group who was suspicious does not include the listener. If the speaker wanted to include the listener (for example, telling a story to a friend who was there), they might say kita.

What is curiga here: a verb or an adjective? And why is tidak used, not bukan?

Curiga is an adjective meaning suspicious or feeling suspicious.
In Indonesian, tidak is used to negate verbs and adjectives, while bukan negates nouns or pronouns.

tidak curiga = not suspicious
bukan guru = not a teacher

So kami tidak curiga lagi = we were not suspicious anymore.

What does lagi mean in tidak curiga lagi?

Lagi often means again, but with negation it usually means anymore / no longer.

curiga lagi = suspicious again
tidak curiga lagi = not suspicious anymore / no longer suspicious

So kami tidak curiga lagi is best translated as we were not suspicious anymore or we were no longer suspicious.

Can I change the word order to kami tidak lagi curiga? Is that still correct?

Yes. Both are correct and natural:

kami tidak curiga lagi
kami tidak lagi curiga

They both mean we are/were no longer suspicious.
Putting lagi at the end is extremely common, especially in speech. Putting lagi before curiga can feel a bit more formal or written, but it’s still very normal.

Could I say Setelah polisi datang memeriksa, ... without dan?

You could say Setelah polisi datang memeriksa kami, ..., but the meaning changes slightly:

datang dan memeriksa = came and examined (two separate actions)
datang memeriksa kami = came to examine us / came and examined us (more tightly linked idea: they came for the purpose of examining)

Without kami, datang memeriksa sounds incomplete or less natural. In the original sentence, dan cleanly links two verbs sharing the same subject.

Can I replace setelah with sesudah or ketika?

Sesudah is almost the same as setelah here.
Sesudah polisi datang dan memeriksa, kami tidak curiga lagi.
This is fine and means the same thing.
Ketika means when (at the time that), not after, so the nuance changes:
Ketika polisi datang dan memeriksa, kami tidak curiga lagi.
→ It suggests that already at the time the police came and checked, we were not suspicious (the change of feeling happens during that time, not strictly after they finished).

Setelah/sesudah emphasize afterwards; ketika emphasizes at the time when.