Learn Russian: Киоск на остановке.

Russian does not have articles like "a" or "the". You figure out which one makes sense from the context. Here, "The kiosk" is the most natural translation because we are talking about the location of a specific kiosk.

The dictionary says the word for stop is остановка, so why does it end in -е here?

When you talk about where something is located using words like на or в, Russian nouns change their endings. This is called the Prepositional case. For most feminine words ending in -а, the ending changes to -е. So, остановка becomes остановке.

Why do we use на instead of в to say "at the stop"?

While в usually means inside a closed space, на is used for open areas, surfaces, and public transit stops. Since a bus stop is an open location rather than a building you go inside, Russian uses на.