Learn Russian: Они изучают испанский язык.

In Russian, when you talk about studying or speaking a language using an adjective like испанский (Spanish) or русский (Russian), you usually include the noun язык (language). Literally, this sentence says "They are studying the Spanish language."

Испанский язык is the object being studied. Shouldn't it change its ending for the accusative case?

It actually is in the accusative case here! Язык is a masculine noun. For non-living (inanimate) masculine nouns, the accusative case looks exactly the same as the dictionary (nominative) form. Because the noun doesn't change, the matching adjective испанский doesn't change either.

I've seen other verbs for "to study", like учить and учиться. Why use изучать (изучают) in this sentence?

Изучать is the best verb to use when you are deeply studying a specific academic subject, a science, or a language. It requires a direct object, meaning you must state exactly what subject is being studied right after the verb.

How do I know if изучают means "they study" or "they are studying"?

Russian doesn't have a separate "continuous" tense like English does. A single verb form like изучают covers both a general fact ("they study Spanish every day") and an action happening right now ("they are studying Spanish at this exact moment"). You just rely on the context of the conversation to know which one is meant.