Camaro SS AC compressor seems stuck, can it be repaired or must I replace it?

I have a question about my car and I hope someone here has been through the same thing. I have a 2016 Camaro SS and I use it every day to go to work. About ten days ago the AC stopped cooling. When I press the AC button, I do not hear the usual click from the front of the engine, and the air stays warm no matter how long I wait. My friend says the compressor is dead and I should start saving money. My cousin has an old Mustang and he said sometimes it is only the clutch or a small fuse that stops the compressor from turning on. I did not know who to believe, so one night I read about it online. I opened a page about Camaro cars on a Sharjah website to learn how the compressor, the clutch and the fuse work together. It said that a compressor that does not start can be a small electric problem, and that a proper test should come before anyone changes a big part. That gave me some hope. Then a coworker told me to look for a Professional Camaro AC compressor repair in Sharjah and ask them to test the power and the clutch first. He said a good place will tell me clearly if the part can be repaired or if it really needs to be replaced. I liked that advice because I do not want to pay for a new part if a small fix is enough. So I have some questions. If the compressor does not click at all, is it usually the clutch, the fuse or the whole compressor? Can a compressor clutch be changed alone, or do garages always sell the full part? Is it safe to try the AC again and again, or can that cause more damage? And about how long does a proper check take, and what is a fair price? If you had the same thing on your Camaro or another American car, please tell me what it was and about how much you paid. Thanks a lot.