baega apaseo oneureun jibeseo swieoyo.

Here 배 means stomach/belly.
Korean has several common words pronounced bae:

• 배(腹) = stomach/belly (this sentence)
• 배(梨) = pear
• 배(船) = boat/ship
  The context 배가 아프다 is a fixed, very common expression meaning to have a stomachache.

With the adjective 아프다 (to hurt / be painful), the body part that hurts is typically marked with the subject marker -이/가:

• 배가 아파요 = My stomach hurts.
  Using 배를 can be possible in some contexts, but 배가 아프다 is the standard, most natural pattern.

-아서/어서 connects two clauses and usually means because / so (cause → result).

• 배가 아파서 = because (my) stomach hurts
  Then comes the result:
• 오늘은 집에서 쉬어요 = I’m resting at home today.

It depends on the final vowel of the verb/adjective stem:

• If the stem ends in ㅏ or ㅗ, use -아서.
• Otherwise, use -어서.
  아프다 → stem 아프- (not ㅏ/ㅗ) → 아파서 (ㅍ irregular contraction happens: 아프 + 어서 → 아파서).

This is a common contraction:

• 아프 + 어서 would be 아프어서, but in real usage it contracts to 아파서.
  More examples of similar contraction:
• 크다 → 커서
• 쓰다 → 써서

오늘은 means as for today / today (in particular).
The topic particle -은/는 highlights a contrast or sets the frame:

• 오늘은 집에서 쉬어요 = Today (unlike other days / for today), I’m resting at home.
  It can imply something like “I usually do something else, but today I’ll rest.”

Korean often omits the subject when it’s obvious from context.
Here, the natural understood subject is I:

• (저는) 배가 아파서 오늘은 집에서 쉬어요.
  Adding 저는 is possible, but not required.

집에서 means at home with emphasis on the place where the action happens.

• -에서 = location of an action (do X at/in Y)
• -에 = destination or static location (to Y / at Y depending on verb)
  So:
• 집에서 쉬어요 = rest at home (action happens there)
• 집에 가요 = go to home
• 집에 있어요 = be at home (existence/state verb)

쉬어요 is the present tense, polite informal form of 쉬다 (to rest / take a break).
It’s appropriate for everyday conversation with strangers, classmates, coworkers, etc.
Other levels:

• Casual: 쉬어
• Polite formal: 쉽니다
• Very polite: 쉬어요/쉽니다 are more common than extra-honorific forms here.

It can cover both, depending on context. Korean present tense often expresses:

• a current/general action: I rest
• a near-future plan: I’ll rest / I’m going to rest
  With 오늘은 and the “because I’m sick” context, it naturally reads as a plan for today: I’ll rest at home today.

Yes, both can mean because, but the nuance can differ:

• -아서/어서 (아파서) is a straightforward cause → result link.
• -(으)니까 (아프니까) can sound slightly more explanatory or reason-giving, and is also common in spoken Korean.
  Both are natural:
• 배가 아파서 오늘은 집에서 쉬어요.
• 배가 아프니까 오늘은 집에서 쉬어요.

A few natural sound shifts happen:

• 배가 is often pronounced closer to [배가] (pretty direct), but the -가 can sound light.
• 오늘은 often sounds like [오느른] (ㄹ liaison-like effect in fast speech).
• 집에서 often sounds like [지베서] because ㅂ can sound like ㅂ/ㅁ-adjacent and vowels flow quickly (not a spelling change—just fast speech).
  A natural rhythm is:
• 배가 아파서 / 오늘은 / 집에서 / 쉬어요 (small pauses by phrase)