sueobi beolsseo kkeutnasseoyo.

이 is the subject marker attached to a noun ending in a consonant. It labels 수업 (“class”) as the sentence’s subject. If the noun ends in a vowel, you’d use 가 instead. Both 이/가 mark the subject, but sometimes they also carry nuance:

• 이/가 often introduce new information or emphasize the subject.
• 은/는, by contrast, can mark topics, show contrast, or indicate known information.

벌써 means “already” and expresses surprise or unexpectedness that something happened sooner than expected. Typical placement is right before the verb or the adjective:

• 수업이 벌써 끝났어요.
  You could also place it at the very beginning for extra emphasis:
• 벌써 수업이 끝났어요?
  That fronting intensifies your surprise.

끝났어요 is the polite past tense of 끝나다 (“to end”). It breaks down as follows:

1. 끝나-: verb stem meaning “end.”
2. -았/었-: past-tense marker. Since 끝나 ends in a vowel + ㄴ, we use 았 → 끝났-.
3. -어요: polite ending (present/past tense). Combined, 끝났어요 = “ended” in polite speech.

The ㅆ is from the past tense marker -았/었-. When you attach 었 to 끝나, the ㄴ and 었 merge into ㄶ sound (pronounced -났-), and the spell-out becomes 끝났. Adding -어요 gives 끝났어요. That ㅆ always signals past tense.

• 끝나다 is intransitive: the subject ends/finishes by itself. (“Something ends.”)
• 끝내다 is transitive: someone ends/finishes something. You need an object. (“I finish the homework.” = 숙제를 끝내요.)
  In your sentence, the class ends on its own, so you use 끝나다.

-어요 is the standard polite ending for informal settings: among adults who are not very close friends or in customer service. It’s neither too formal nor too casual.

• Use -습니다 for very formal or written announcements.
• Use -아/어 for close friends or younger people.

Yes. If context is clear, you can drop 수업이:

• 벌써 끝났어요.
  This is common in everyday speech. It sounds more natural if everyone knows you’re talking about the class.

Simply change the statement to a question tone:

• 수업이 벌써 끝났어요?
  Or less polite/familiar:
• 수업이 벌써 끝났어?
  Or more formal:
• 수업이 벌써 끝났습니까?