1. 모든 사람들이 누구나 실수를 다 하지만 이 실수를 만회하는 것만 중요해요.
(Everybody makes mistakes but it's important to make up for them/fix the errors we've commited)
I would be grateful for some other sentence examples with similiar meanings If possible!
모든 사람들이 누구나 실수를 다 하지만 실수를 만회하는 것이 더 중요해요.
이 실수 means particularly 'this' mistake, so it is good to say just 실수 mistakes, to make it more general
~는 것만 means also very limited meaning, everything is not important except correcting. but by saying but(하지만) ~는 것이 (correcting those mistakes ) 더 중요해요 (are more important)
umm we also say, 결과보다 과정이 더 중요하다(it is more important how you did than the result)
and also we say your sentence a lot ^^
2. 편지 쓰면서 "소식 기다리겠습니다" 쓰는 것(은) 괜찮(은) 것 같아요? 그 사람에게 직접적(인) 대답(은) 안 받을거예요.
When writing a text message/letter to somebody from whom you won't receive a direct answer (a celebrity or higher figure) is it okay to say 소식 기다리겠습니다? Or is it too formal? Is there any other way to say "Hope to see and hear from you soon" (it sounds not too formal, but it's okay if in Korean it sounds either way)
Umm... I think mentioning the answer(소식) makes people feel that they should answer. and especially you said a very formal way, If I got your message then I would reply. and it is ok I usually say 소식 기다리겠습니다 to my professors when I send an email to them. and you can say it 연락 주시면 감사하겠습니다. (it will be pleasure if you reply to this message)