Learn Hardcore Indonesian: Alih-alih panik, kami telah duduk tenang dan mendengar instruksi. - Instead of panicking, we have sat calmly and listened to the instructions.

duduk tenang: natural; “sit calmly.”
duduk dengan tenang: slightly more explicit/adverbial; same meaning.
duduk diam: “sit still/quietly” (focus on not moving/talking), not necessarily “calm.”
tetap tenang: “stay calm” (not about sitting specifically).

It means instead of. The hyphen is standard (per PUEBI): alih-alih. Writing alih alih without a hyphen is nonstandard. It often starts a sentence or clause to contrast two options.

Is the comma after Alih-alih panik necessary?

Recommended, yes. You’re fronting a contrastive phrase, so a comma helps readability: Alih-alih panik, .... If you insert alih-alih mid-sentence, set it off with commas: Kami, alih-alih panik, ....

Is panik a verb here? Could I say berpanik or memanik?

In Indonesian, panik typically functions as a predicate adjective (stative): Mereka panik “They panicked/are panicking.” Forms like berpanik or memanik are not standard. For “to become panicked,” you can say menjadi panik. For the noun “panic,” use kepanikan.

Why use kami and not kita?

kami = we (excluding the listener)
kita = we (including the listener) Here, kami implies the listener was not part of the group that sat and listened.