A: Yes, Korea is very safe to travel.
As a Korean, we pride ourselves on being a pretty safe country. In fact, I have traveled to the United States for about 3 months. At that time, I learned how safe Korea is and how friendly it is to travelers. I've been through a lot of really absurd things that I couldn't get it in America, but I won't mention it here.
There are many places in Korea that open 24 hours a day. Strictly speaking, it is mainly in big cities like Seoul or Busan. Many people go shopping at night, meet up with friends, and go out to the downtown area to hang out with their friends at cafes, restaurants, and bars that are open 24 hours a day. Especially on Friday or Saturday nights, this place is crowded with many people until late at night and even in the morning. It is an excellent environment for people who really enjoy nightlife like drinking and dancing at clubs or bars. This means security is relatively good enough to enjoy the nightlife compared to other countries.
What's even more surprising is that if you've left something on the subway or in a cafe, your stuff will remain there or you can find it mostly by asking the counter staff. In Korea, the culture of taking up a seat is ordinary life. It's not unusual to leave your own items and go to order at the counter. Having an object means that someone else has already chosen this position, so no one touches it.
Another reason is that most people know that there are surveillance cameras everywhere out there, so we know it's better not to take things with them.
Even in the case of a hotel, if you have lost your items in the hotel and left behind, the housekeeper will keep them or they will be stored in a storage room, so you can ask at the staff in the hotel or you can go to the lost and found center and check if your lost item is stored.
Also, if you don't know where you've lost your stuff, wait and see. You may be contacted by phone or mailed if you put your contact number in your wallet or valuables, you're much more likely to get them back.
So Don't worry. Korea is really safe to travel.