So a lot of these units conduct courses from unit funds in isolation.. and these trainers after teaching one course at the unit will put it up on their website to boost their credibility.
If you ask who is training Indian SOF units on a regular basis, thats Kanishka Sharma. His syllabus is implemented for students at most of these units, and also at SFTS, Nahan. And there is a cadre of CQC instructors from amongst Para SF, who teach CQC at Nahan, they keep coming periodically to this guy for continuous skill development.
With regard to your question about firearms training, anybody with enough money, and a basic level of skillset can go abroad and do courses from places like EBSSA, and become qualified enough to teach these units with enough practice put in on ranges. Especially, if you plan on doing this as a career.