Question

1. She is good at dancing.
2. She is good at dance.

(Which one is correct? Are both correct?)

3. I am a student at Class 1-1.
4. I am a student in Class1-1.
5. I am in Class 1-1.
6. I am a first year student in Class
1-1.
7. I am a first grader of Class 1-1.

(Are all grammatical?)

Answer 1

1. and 2. would have slightly different meanings. 2. would apply to someone studying dance as a career, as in ballet. "dancing" usually refers to social dancing in pairs.

3. is not grammatical.
6. and 7. may be redundant, if "Class 1-1" is one of the first grade classes. Still, 6. is OK, but 7. is awkward. It sounds like you are studying the class itself.