1. True, a significant number of people have shown speedier recovery with hypnosis, and surgical wounds heal faster. But the same has been seen with prayer. And zen meditation.
2. True, many athletes—and musicians, and dancers—have used hypnosis to overcome performance anxiety. The same can be said of Bach flower remedy. Or, again, zen meditation.
3. False, not everyone can be hypnotized. Probably the biggest reason is that one must be willing, otherwise no attempt at hypnosis is going to be effective.
4. Of course true, many people believe the effects of hypnosis come from people believing it will work. And the same can be said of prayer, and Bach flower remedies, and meditation, etc...
There is evidence that the mind can influence healing in the body. Perhaps the effectiveness of hypnosis is primarily or entirely due to the expectation that it will work. Perhaps that is the definition of hypnosis anyway.