1.  The answer is (C). To answer this question, you need to understand the usage of polite and plain forms in Korean.

2.  The answer is (A). The question tests the usage of a noun modifying construction such as the -(으ㄴ/-(으)ㄴ/-는/-던 form followed by a noun.

The answers for 3-5 are:

3.  성희가 할머니께 보내는 편지
4.  가방
5.  할머니의 생신을 축하하기 위해서.