Learn Hardcore Indonesian: Setelah kabut hilang, keputusan kami tetap: latihan kebugaran dilanjutkan. - After the fog disappears, our decision remains: the fitness training is continued.

Setelah is a conjunction meaning after, introducing a time clause: setelah kabut hilang = after the fog disappeared.
You can generally replace setelah with sesudah without changing the meaning:

Setelah kabut hilang, ...
Sesudah kabut hilang, ...

Both are correct; setelah is a bit more common in writing, but the difference is very small.

Why is it kabut hilang and not kabut menghilang or kabutnya hilang?

All three are possible, but with slightly different nuance:

kabut hilang – very natural and neutral; literally fog disappear; hilang works like an intransitive verb to disappear here.
kabut menghilang – also means the fog disappears, but menghilang is a verb derived from hilang; this can sound a bit more dynamic or literary.
kabutnya hilang – the fog is gone / has disappeared, with -nya making it more specific (the fog) and sometimes more colloquial or situational.

In this sentence, kabut hilang is a clean, neutral choice.

What does keputusan kami tetap mean exactly, and how does tetap work here?

Keputusan kami means our decision.
Tetap means remain / stay (the same). So keputusan kami tetap literally means our decision stays (the same) or our decision remains unchanged.
You could also say keputusan kami tidak berubah (our decision did not change), which is a bit more explicit but similar in meaning.

Why is there a colon after tetap: keputusan kami tetap: latihan kebugaran dilanjutkan?

The colon introduces an explanation or a specific content of the decision.
You can read it as: Our decision remained as follows: the fitness training would continue.
This use of the colon is very similar to English punctuation.

What kind of phrase is latihan kebugaran, and how is it formed?

Latihan kebugaran is a noun phrase meaning fitness training / workout.

latihan = practice / training, from the root latih (to train).
kebugaran = fitness, from bugar (fit, fresh) + ke- -an (a noun-forming prefix/suffix).

Together, latihan kebugaran literally means training (of) fitness.

Is dilanjutkan passive? Who is actually doing the continuing here?

Yes, dilanjutkan is the passive form of melanjutkan (to continue [something]).
In latihan kebugaran dilanjutkan, the logical subject (the doer) is not mentioned; it’s understood from context (for example, kami or the organizers).
So it corresponds to English passive: the fitness training was continued / would be continued.

Could I say this sentence in active voice instead of passive?

Yes. An active version could be:

Setelah kabut hilang, keputusan kami tetap: kami melanjutkan latihan kebugaran.

Here kami is explicitly the subject of melanjutkan.
The original passive version sounds a bit more formal and focuses on latihan kebugaran (the training) rather than on kami.

There is no tense marker like sudah or akan. How do we know the time of the actions?

Indonesian usually relies on context and time expressions instead of verb tense.
Here, setelah kabut hilang already gives a sequence: after the fog disappeared. That implies a past situation leading to the decision.
You could add markers if you really want to emphasize it:

Setelah kabut sudah hilang, ... (after the fog had already disappeared)
Latihan kebugaran akan dilanjutkan. (the training will be continued)

But they are not necessary; the basic sentence is already clear.

Why is kami used instead of kita?

Both mean we, but:

kami = we (not including you, the listener).
kita = we (including you, the listener).

Using keputusan kami suggests the decision belongs to a group that does not include the person being addressed (for example, the coaches or committee talking to the participants).

Can I change the word order and put the setelah-clause at the end?

Yes, you can say:

Keputusan kami tetap: latihan kebugaran dilanjutkan setelah kabut hilang.

This is still correct and natural.
Putting setelah kabut hilang at the beginning gives a bit more emphasis to the condition/time, but both orders are acceptable.

How would a more casual version of this sentence look?

A more conversational version might be:

Begitu kabut hilang, kami tetap lanjut latihan kebugaran.
- begitu here = as soon as / once
- tetap lanjut is a more casual way of saying continue as planned

You could even shorten further in very informal speech:

Begitu kabut hilang, kita lanjut latihan. (if the listener is included in kita).