#1. 쓸데없이 잘생겼다. 잘생겼다 part is obviously a compliment, but adding 쓸데없이 makes it a joke or an intentionally twisted remark rather than adding or taking away compliment. One cannot seriously connect the concept of 쓸데없이 and 잘 생겼다. There are many nonsense lines like this: 잘생긴 것도 죄냐. 못생겨서 미안하다. 아예 안 생겼다, etc. #2. 쓸데없이 literally means "uselessly" (쓸: to use, 데: place/purpose 없이: without). So one can use it for any action done without a purpose or utility. - 쓸데없이 여러 말을 하거나 묻지 않다. - 쓸데없이 남의 일에 끼어들지 말고 네 일이나 열심히 해라. #3. 쓸데없이 means uselessly, needlessly, or "without purpose or utility". 괜히 means "without reason" or "for no reason" primarily. They have some overlap in meaning and can be used interchangeably however. #4. 나 쓸데 없이 한국말 배우고 있는것 같아. It is correct but strictly speaking you should write "나 쓸데없이 한국말 배우고 있는 것 같아" (띄어쓰기 - spacing issue). 쓸데없이 is one word, while "있는 것" is not. It is a fine point that even many Koreans sometimes don't follow but nevertheless the official rule.