Some countries are exempt from visa to visit South Korea. These countries are EU countries, Antigua & Barbuda, The Bahamas, Bangladesh, Barbados, Brazil, Bulgaria ..... Etc. You didn't mention here about your nationality.
You need a valid passport, one recent passport size photograph, completed application form, proof of sufficient funds etc to apply for the visa.
For complete details about the documents, click this link
I don't know but you might need a big coat because my friend is from South Korea and she says it is cold and sometimes cold in the summer so maybe something warm just in case.