Learn Hardcore Russian: Мы идём по тропинке, пока не увидим озеро. - We are walking along the path until we see the lake.

идём: the <a class="border-b border-dotted border-blue-400 dark:border-blue-500 cursor-pointer text-inherit no-underline" href="/grammar/russian/writing-system/yo-letter">ё is always stressed and pronounced yo → roughly ee-DYOM
уви́дим: stress on the second и → oo-VEE-deem
тропи́нке: stress on и → tra-PEEN-ke
о́зеро: stress on the first о → O-zi-ra

Идём is the 1st person plural of идти (one-direction movement) and fits a single, concrete trip: we’re going/walking (right now / on this occasion).
Ходим is from ходить (multi-direction / habitual) and would sound like we (generally/regularly) walk along the path, not one specific walk to a goal.

What case is по тропинке, and why?

After по meaning along / on (a route), Russian commonly uses the dative case.
So тропинка → dative singular тропинке: по тропинке = along the path/trail.

Does по тропинке mean “on the path” or “along the path”?

In this context it’s best understood as along the path / following the path. It can often be translated as on the path in English, but the Russian image is “moving along it as a route.”

Why is there a comma before пока?