Learn Hardcore Korean: jeoneun maeil achim 30bunssik doseogwane danyeoyo. - I go to the library every morning for 30 minutes.

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).

Why is the verb 다녀요 used instead of 가요?

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.

Why is the particle 에 attached to 도서관?

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).

What function does 저는 serve, and why is 는 used instead of 가?

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.

How is the word order (time, duration, place, verb) organized in this sentence?

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)

Is there a difference between 매일 아침 and 아침마다?

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.

Does this sentence imply that I study in the library?

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.