Anesthesiology

The two fields are completely different. The only way you can decide what you like is by doing an elective and see what you like better. Honestly, I think too many people go into anesthesia because they think it's going to be low stress, and later realize it can be very stressful and become very unhappy. I'm sure radiologist, and anesthesiologist, will figure out a way to more money when the cuts come. So, be honest with yourself and do what is most interesting, rewarding, etc.

Anaesthology is offered only as a post-graduation subject after completing MBBS. However, you can do B.Sc Anaesthesia technical course from various institute such as Amruta University, Manipal, Narayan Hridayalaya, etc.

Yes, you can, after your class 12th (PCMB).
Apply online or offline on the institute website.
Look for institutions like Amrita Institute Kochi, Agartala Government Medical College, and Aligarh Muslim University.

Some of the colleges which I can suggest are- Amala Institute of Medical Sciences, Amrita Institute of Medical Science, Amrita Institute of Medical Sciences and Research Centre, Government Medical College, etc.

Both are equally good courses, you have to choose according to your interest only. After doing both courses, you have good job options. You may get both government and private jobs. The only difference is that after doing BPT, you will be designated as a doctor and you can do your own practice and after nursing, you will be known as a nursing sister only but both have good career scope in future.