Learn Russian: Подросток стоит среди взрослых. - The teenager is standing among the adults.

The preposition среди (among) always requires the Genitive case. Since there are multiple adults, we use the Genitive plural form, which is взрослых.

взрослых looks like an adjective, but means 'adults' here. Why does it have that ending?

взрослый is actually an adjective meaning 'grown', but it is often used as a noun to mean 'an adult'. Because it is still grammatically an adjective, it takes standard adjective endings. That is why its Genitive plural is взрослых, matching the ending you would see in adjective forms like новых.

Is the word подросток (teenager) related to the Russian words for growth?

Exactly! It contains the root -рост- (growth or height), which you might recognize from the verb расти (to grow). A подросток is literally someone who is in the process of growing up.

Could I just say находится (is located) instead of using стоит (is standing)?

You could, but Russian strongly prefers verbs that describe physical posture, like стоять (to stand) or сидеть (to sit), when placing people in a scene. It sounds much more natural and descriptive than just saying someone 'is located' there.