Any common/ useful 한국말 phrases?
Are there any common or useful Korean phrases that I could use? As in for example, in Japanese, they use lots of phrases (even in their TV Shows) like "Shouganai" -- "It can't be helped". Or "Natsukashi" -- "This is nostalgic" and these are common in Japan.

What about Korea?
(Just any and every phrase you can think at the top of your head would be fine.) 주세요... 감사합니다!
한글으로 쓰기하세요.

Question

Any common/ useful 한국말 phrases?
Are there any common or useful Korean phrases that I could use? As in for example, in Japanese, they use lots of phrases (even in their TV Shows) like "Shouganai" -- "It can't be helped". Or "Natsukashi" -- "This is nostalgic" and these are common in Japan.

What about Korea?
(Just any and every phrase you can think at the top of your head would be fine.) 주세요... 감사합니다!  
한글으로 쓰기하세요.

Answer

"Common/ useful 한국말 phrases"

That sounds too broad.  So I'll give you Korean versions of the ones you mentioned and some others.

- Shouganai (It can't be helped) - 할 수 없어 / 어쩔 수 없어.
- Natsukashi (I miss [that time / those days]) - (그때가) 그리워 / (그 시절이 / 옛날이) 그립다.

Here are some phrases about hope, future, and time.
- 내일은 내일의 해가 뜬다 - Tomorrow will have tomorrow's sun (Tomorrow is another day).
- 미래는 꿈꾸는 자의 것이다 - The future belongs to those who dream.
- 희망의 샘은 영원히 샘솟는다 - Hope springs eternal.
- 세월 이기는 장사 없다 - Nothing in the world beats time.
- 세월이 약이다 - Time cures everything.
- 이 또한 지나가리라 - This will pass too (Nothing lasts forever).

And here's how you might say the last sentences of your post:
"(Just any and every phrase you can think at the top of your head would be fine.) 주세요"
=> 그냥 머리에 생각나는 [떠오르는] 대로 말해 주세요.

"한글으로 쓰기하세요." => 한글로 써 주세요.  (으로 after a syllable of ㄹ 받침 or no 받침 becomes 로)