Here are your questions followed by answers.
1. Is a hypnotist to a psychologist (or psychiatrist for that matter) what a chiropractor is to a doctor?
No, hopefully, a hypnotist has become a psychologist, clinical social worker, marriage and family therapist, or psychiatrist as most state laws require. The therapists choice to use hypnosis is parallel to their choice to use behavior modification, gestalt therapy, group therapy, etc. It is a mode of communication and information exchange.
2. Does hypnotism really work? (eg trances)
Work to do what? It does not do anything. It is a mode of communication and information exchange. As such it “works” to be a different context for communicating, yes.
a. Does hypnotism simply allow a person to speak their feelings without being embarrassed?
No. Hypnosis allows a person to relax their customary reality orientation. While this can result in speaking without social anxiety, a much much more important aspect of the circumstance is the client’s ability to associate (of dissociate for that matter) experiences. So, to be general, the experience of being confident can be associated to the perceptual context of public speaking…thus making the learning of the experience in that context achievable.
3. Is there a scientific method for proving that a person is in a state of hypnosis?
No. Hypnosis proves out to be more like waking state than any other by the current means of physiological testing. It would be a great boon for the field if a detectable and undeniable correlate could be uncovered.
4. What about those infomercials in which an entire crowd is "hypnotized"? What is the professional viewpoint on that?
People hypnotize themselves with the aid of the operator. All (ALL) hypnosis is self-hypnosis. The people in a particular setting may have similar enough motives to all participate. There is a nice book on the subject of group hypnosis in which indications by Kay Thompson, Lankton and Lankton, etc., are exemplified.
5. Is NLP the only major theory of hypnosis? Is there another one?
NLP is not generally considered a theory of hypnosis. There are several, yes. Bernheim, Sabin and Coe, T.X. Barber, Hilgard, Speigel, Tart, etc., are some of the names associated with major theories. Some of the names they go by the names of “therapeutic suggestion,” “social role,” “neo-dissociational,” “state,” etc., to name a few. There is a bushel of research about each and about their relationship to each other in every which way.
6. I apologize if my questions seem loaded (or ignorant of established paradigms)... but i'm earnestly looking for answers from professionals who sit on both sides of the fence.
The questions suggest that you are not a professional in the field. Curiosity is a valuable thing. However, let me use this opportunity to remind, it is not appropriate to practice hypnosis without a solid grounding and license in and the helping professions and proper training in the field of hypnotherapy. Thanks for excellent questions!