날 / 일 both mean "day" but the first is native Korean word and second is Sino-Korean (inherited from Chinese). 날 has broader use but 일 is also used for document type stuff like dates and calendars. 일 also means Sun (the sun could also be called 태양 or 해).

낮 is daylight hours, sunrise to sunset.

하루 is a 24 hour day. For example, to say "every day" you'd say 하루마다 and "day-by-day" 하루 하루.

And then there's also 오늘 which means "today."

There's also plenty of words for X days later/ago. 어제 / 그저께 yesterday, day before. 내일 / 내일 모래 tomorrow, day after. I can't remember the three or four count words...