1. 지 마(요)/ 지 말아요
It's an exception, 말다 conjugates to 마, not 말아.
In the same way, 마라 is the "correct" version of 말아라 :)
2. 이걸 주세요
이거로 주세요
-를 just indicates a direct object
이걸 (이것을) 주세요 "Give me this one please"
-로 indicates an instrument, comparable with the preposition 'with'
You should never try to translate it directly to English
이거로 (이것으로) 주세요 "I'll go with this one please"
3. 갖다 팔면 한 재산은 되겠어요.
갖다 here is short for 갖다가
가져다 주세요.
It's one verb, 가져다주다, there's others like 데려다주다
I don't think you should really pay attention to the structure of this verb, just see it as one verb as a whole
4. 왜 이래요?
이래요 is conjugation of 이러다 (이리하다) meaning 'to do/act like this'
So it means "why are you acting like this"
Don't confuse it with 이렇다 which also conjugates to 이래요 but means "to BE like this"
5. 이런데 / 이런곳/ 장소 /군데
Sorry I'm not familiar with these nuances
6. - 딴 생각 안 하게 일이나 열심히 하려고요.
-게 has several meanings, here it means "so that"
- 이런 일로 심려 끼쳐드리지 않게.
Is this song lyrics? I think it also means "so that"
- 생각지도 못하게
Here it also means "so that"
when does "게" change "adj" into "adv'
when does "게" mean "let sb do"
You'll always have 하다 or 만들다 after the -게 when it means the latter
생각하게 하다 to make smb think
Otherwise, it turns adjective verbs into adverbs
크게 소리치다 to scream loudly
7. 이름후에 “이” 무슨 뜻인지?
It's just affective, like calling your friend Stephanie 'Stephie'
이름후에 “양” 무슨 뜻인지?
It means Miss
8. 나가거라/ 나가라
Naverdic says -거라 gives an archaic feeling compared to -어라
9. 그는 집을 나간단다. neutral (나간다고 한다)
그는 집을 나간대. informal (나간다고 해)
그는 집을 나간답니다. formal (나간다고 합니다)
They all mean "(They say) he's leaving home"
I'm putting "they say" between parentheses because it seems like Koreans sometimes use this construction for no reason
10. 어딨, 재밌어, I sometime read this words, can you pls show me some other
I think these 2 are the most common ones