Learn French: Certains animaux s'adaptent, cependant le milieu reste difficile. - Certain animals adapt, however the environment remains difficult.

Yes, you absolutely can. Both are used to express opposition or contrast. cependant (however) simply links two contrasting facts. pourtant (yet) is slightly stronger and emphasizes that the second fact is surprising given the first one. Here, both fit naturally.

Why is the verb reflexive (s'adaptent) here? Can I just say Certains animaux adaptent?

You need the reflexive pronoun s' because the verb adapter requires a direct object. You have to adapt something. When animals adapt themselves to a new situation, you must use the reflexive form s'adapter.

I thought the word for environment was l'environnement. Why use le milieu here?

L'environnement typically refers to the environment in a broad, ecological sense, like when talking about climate change. Le milieu is used to talk about a specific habitat, setting, or the immediate physical surroundings an animal lives in.

In English, using a comma before however often creates a run-on sentence. Is this comma correct in French?

Yes, it is perfectly correct. French punctuation is a bit more flexible with connectors. Joining two independent clauses with just a comma and cependant is completely standard in French, even though it might be considered a comma splice in English.