Learn Hardcore Korean: bame iljjik jayo, geuraeseo da-eum nal pigonhaji anhayo. - I go to sleep early at night, so I'm not tired the next day.

밤에 means “at night.” The noun 밤 (“night”) takes the location/time particle -에 to indicate when something happens. So 밤에 specifies the time frame for the action "sleep."

Is 일찍 an adjective or an adverb, and how is it functioning in this sentence?

일찍 is an adverb meaning “early.” It modifies the verb 자요 (“sleep”). In Korean, adjectives that end in -다 can often become adverbs by simply using their stem (in this case 일찍) before a verb.

Why do we use 자요 instead of 자 or 잔다?

자요 is the polite present tense form of the verb 자다 (“to sleep”).

자 is the basic present tense informal form (used with close friends or younger people).
잔다 is the declarative (plain) style often used in writing or narrating.
Since the sentence is polite and conversational, 자요 is appropriate.

What is the function of 그래서 and why is there a comma before it?

그래서 means “so” or “therefore.” It links the first clause (going to bed early) to the second clause (not being tired). The comma separates the cause and effect clauses, making the sentence flow smoothly in writing.

How does 다음 날 differ from 내일, and why use 다음 날 here?

내일 specifically means “tomorrow.”
다음 날 literally means “the next day” and can be used in broader contexts (e.g., describing events in a story).
In spoken Korean, 내일 would also work, but 다음 날 adds a slightly more descriptive or narrative tone.

Explain how 피곤하지 않아요 is formed.

피곤하다 is the adjective “to be tired.” To make it negative in polite speech, you:

Drop -다 → 피곤하-
Add the negative marker -지 않다 → 피곤하지 않다
Conjugate in polite present tense → 피곤하지 않아요 (“is not tired”).

Why is the verb 않아요 placed after 피곤하지 instead of directly negating 피곤하다 as 피곤안해요?

Korean uses the auxiliary construction -지 않다 to negate verbs and adjectives. You cannot simply stick 안 in front of every adjective stem. For 피곤하다, the correct negative is 피곤하지 않다, not 안 피곤하다 (though informally you might hear 안 피곤해요, the -지 않다 form is more standard and transparent for learners).