Certain grammatical points will be covered in the sessions and you will research particular areas related to your lesson aims, but the main focus of the CELTA is teaching techniques and frameworks, i.e. how to teach grammar, rather than specific areas of grammar itself..
No. The course is open to non-native speakers. However, you must have sufficient competence in English to interact comfortably with native and proficient speakers on the course, so your English should be at the Pre-Advanced level.