In theory, $1 is more like 1,100W. But, to keep it simple, just think 1,000W to 1$ and drop the extra three zeros.
Kimbap shop is not the proper name of the restaurant. You're looking for something like this (pictures and menu information in the link below). There are many different chains, but this one is the most common name. Other chain names are Kimbap Nara and Pomato.
https://www.google.co.kr/webhp?sourc...bap%20cheonguk
I would not bring cash from the States, because the exchange rate always changes here. Sometimes the dollar is up, sometimes it's down. It's not unstable, but it just might vary by the time you arrive here. At the airport, you can withdraw cash at an ATM and get the best rate. The ATMs here don't charge as much as they do in America for sure.
Yes, VISA and Mastercard are accepted everywhere except by street vendors. Also, when you add money to your T-Money card, you must add with cash. The stores won't charge you any fee. Of course, your bank might for using it overseas. Don't count on AmEx and Discover working here.