1) Yes and no, depending on what you mean by "real thing".

The Oxford Handbook of Hypnosis is a giant tome of scientific knowledge on "hypnosis"; none of which suggests that it's not real. Hypnotists really can do seemingly wild shit that most people cannot do. Most hypnotherapists like to say "It's not mind control like Hollywood depicts", but even that is only partially true. The lawyer Michael Fine used hypnosis to sexually assault his clients and give them amnesia for it, and he is in prison now only because he was dumb enough about it that his victims were able to notice that they were missing memory and that things didn't add up. I've talked to victims of more clever hypnotists who haven't gotten caught.

At the same time, there's a reason hypnotists tend to write book with subtitles like "there's no such thing as hypnosis". I'd argue that it's more accurate to say "there's no such thing as not-hypnosis", but neither really conveys an accurate understanding. The bottom line is that hypnosis isn't what it appears to be, because "not hypnosis" isn't what it appears to be, and once you get familiar with how to do hypnosis and see all the gray area between the black and white, the term kinda loses meaning. Competent hypnotists have a strong tendency to drop all the formalisms, and the most competent have a tendency to stop seeing what they do as "hypnosis" -- at least, in my judge of competence as someone who also doesn't see what I do as "hypnosis".

2) Yes and no. I've gotten some interesting results using "self hypnosis". One that stands out is using self hypnosis to "be comfortable" when I was seasick on a rocking boat one night. It worked, and I got comfortable -- only to feel myself about to vomit anyway. Careful what you wish for.

The hard part isn't "Can hypnosis be used to get my brain to believe X", it's what's true? What's worth doing? Are things going well, relative to the relevant expectations? The more you try to bullshit yourself, the more you'll a) have unintended effects if you succeed, or b) foresee this and find it hard to get yourself to do self hypnosis. The more you see clearly what the right answer is, the less you'll need hypnosis in the first place. The real value in learning hypnosis is as a proof of concept that allows you to see when you're BSing yourself so you can stop that.

Due to the counter-intuitiveness and subtleties here, it's hard to give a less cryptic short answer. I'm actually finishing up a ~20 post 65k word sequence on essentially this exact question. It's about what I've learned about psychology and rationality as a result of picking up hypnosis in 2010. It will give concrete and actionable answers to what you're looking for here, as well as the underlying justification. I have a draft done and basically waiting for a proof reader to make it through, then I'll start posting.
 

1. There's a wide range of techniques and behaviors that can be called "hypnosis", and an even wider range of what can be called "a real thing, right?".  Things in the realm of hypnosis (meditation, guided-meditation, self-hypnosis, daily affirmations, etc. have plenty of anecdotal support from adherents, and not a lot of RCTs or formal proof of who it will work for and who it won't.
2. There's a TON of self-help and descriptive writing on the topics of meditation and self-hypnosis.  For many people, daily affirmations seem to be somewhat effective in changing their attitude over time.  For many, a therapist or guide may be helpful in setting up and framing the hypnosis.