2. GRE courses in New Oriental are very targeted. If you don't take the GRE, to be honest, it doesn't make much sense to take the GRE course. If you just want to improve your English, New Oriental still has many courses for you to read.
If you want to strengthen your writing ability, I suggest that you can take up and down listening, speaking, reading and writing classes, and improve your English ability in all directions in the process of teaching and learning.
3. There is generally no homework in the courses of New Oriental. You can buy some exercises yourself if necessary.