jeoneun maeil achim 30bunssik doseogwane danyeoyo.

• 30분 literally means “30 minutes.”
• The particle 씩 after a number or quantity indicates “per” or “each time.”
• So 30분씩 means “for 30 minutes each time” (i.e. each time I go, it’s a 30-minute visit).

• 가요 simply means “go.”
• 다니다 (다녀요 in the polite present) means “to go regularly/attend” or “go back and forth.”
• By using 다녀요, you emphasize that it’s a habitual, repeated action: you go to the library every morning and come back.

• 에 is the location marker used with motion verbs (가다, 오다, 다니다).
• It indicates your destination: “to the library.”
• Note: When time expressions like 아침 act as adverbs, you can often drop 에 (you could say 아침에 but here 매일 아침 works as an adverbial phrase without 에).

• 저 = “I,” and -는 is the topic marker, so 저는 means “as for me.”
• Korean often frames sentences by introducing a topic first (what or whom you’re talking about).
• -가 marks a new or contrastive subject, whereas -는 sets the scene for a statement about the topic.

Korean generally follows:
1) Time expressions → 2) Duration expressions → 3) Place expressions → 4) Verb
In your sentence:
1) 매일 아침 (every morning)
2) 30분씩 (for 30 minutes each time)
3) 도서관에 (to the library)
4) 다녀요 (I go/attend regularly)

• Both mean “every morning.”
• 매일 아침 = “every day’s morning” (focus on each day).
• 아침마다 = “morning-every” (focus on each morning).
• In practice they’re interchangeable in this context.

• No, it only states the habit of going to (and from) the library for 30 minutes each morning.
• To say “I go to the library to study,” you could add 공부하러:
  저는 매일 아침 30분씩 공부하러 도서관에 다녀요.