2. What reasons do trans people give for wanting to change their physical bodies? As in what do people believe they will get from this that they couldn't get in the body they were born with?
This is where it gets really strange.
Children with gender dysphoria generally seem to start with identifying with the stereotypes of the opposite sex. Once those children get the idea that the things they like are only for the opposite sex, they start to want to be the opposite sex and at some point they get the idea that that means their bodies would have to change. If they are told that they can change sex by having medical treatment, they start to want that.
Of course, if we left these children alone, they wouldn't need any body modifications at all because they could just be themselves in their own bodies.
Adults who identify as transgender, in particular older males, often don't want any changes to their bodies at all. They want to wear stereotypically female clothing and to force everyone to refer to them as women, and their penis becomes a 'female penis'.
Aside from all this, it appears that there may be a very tiny number of people who have a disorder, which may be neurological rather than psychological in origin, and makes them feel that their bodies are 'wrong', in the same way as a tiny number of people feel that some body part (such as one of their limbs) doesn't belong to them. For these people, treatment is required, and physical transition may be the most appropriate thing for them.