쥐구멍에도 볕 들 날 있다.

Yes, although it's an old proverb, it's still very common in daily conversation, K-dramas, and even webtoons.

It's a bit informal for a standard business email, but it can be used in a 'cheer up' message to a close colleague or in a speech.

'햇빛' is the general word for sunlight. '볕' is a more traditional/poetic word that often implies the warmth or the 'patch' of sun on the ground.

The standard proverb uses '볕 들 날' (future/potential). '볕 드는 날' sounds like a literal description of a sunny day.

Yes! You can say '드디어 나에게도 쥐구멍에도 볕 들 날이 왔어!' (Finally, my day has come!)

Not exactly, but '달도 차면 기운다' (Even the moon fades after it's full) is a proverb used to say that good times don't last forever.

Mice were common in old houses, and their holes represented the smallest, most insignificant, and darkest parts of the home.

While it emphasizes luck, in Korean culture, it's usually said to people who are *already* working hard but not seeing results yet.

It might be a bit too casual. Instead, use '고생 끝에 낙이 온다는 말처럼...' to show your perseverance.

It's better to avoid it unless you are very close. Using proverbs can sometimes sound like you are 'teaching' the other person.