I have a question about the sentence 늦게 보내서 미안해요.
I know that it basically means 'Sorry for the late answer' but I'm not sure what's the role of '게' and '서' in the sentence. I think adding 게 to 늦 is kind of like adding "ly" to it like 행복하다 /행복하게 = happy/happily so it's kind of like 'Sorry for answering slowly' and I think 서 means 'for' in this case (like 'sorry for...'). Are these correct?

Question

I have a question about the sentence 늦게 보내서 미안해요.
I know that it basically means 'Sorry for the late answer' but I'm not sure what's the role of '게' and '서' in the sentence. I think adding 게 to 늦 is kind of like adding "ly" to it like 행복하다 /행복하게 = happy/happily so it's kind of like  'Sorry for answering slowly' and I think 서 means 'for'  in this case (like 'sorry for...'). Are these correct?

Answer

Jó napot kívánok!

Sorry for the late answer 
literally means
늦은 대답때문에 미안해요.

늦게 보내서 미안해요. = 늦게 보냈어요. 그래서 미안해요.
The word to word translation is
I sent it late, so I'm sorry.

늦게 means "late(adverb)". It is an antonym of 일찍(early)
늦게 is from 늦다(late)

BTW, there is also a word 느리게. it is an antonym of 빠르게(quickly)
느리게 means "slowly"
느리게 is from 느리다(slow)

-서 is a connection suffix of meaning "so, thus".