I think you're conflating sex and gender as used in the DSM V.
en.wikipedia.org
Of course, gender dysphoria is a mental condition. You should agree with that. The very definition makes clear that the person has a defined sex (determined by biology), but a mental condition that makes them uncomfortable with the gender typically assigned to that sex and that makes them identify with the opposite gender. Quite frankly, I don't even know what the far-left trans-activists think about this distinction--I think some argue that sex is not even a real thing (which is inane).
As for support, that is a universal psychiatric goal for all patients, including those with violent tendencies, schizophrenia, etc. It sounds like you are suggesting they should also seek to eliminate the gender dysphoria. I'm not sure that is possible or the history of attempts to end it.
Regarding your question about sexual attraction, as I understand it, all of our sexual attractions are affected by biology and psychology, with our psychology a result of both our genes and biology and external environmental factors.
Regarding conversion therapy, it can cause harm. For all the reasons you state about risk of harm, misdiagnosis, age of the patient w/r/t hormone therapy and sex reassignment surgery (which I agree with), I find it a better idea to take that off the table for children:
Overview: We identified 47 peer-reviewed studies that that met our criteria for adding to knowledge about whether conversion therapy (CT) can alter sexual orientation without causing harm. Thirteen of those studies included primary research. Of those, 12 concluded that CT is ineffective and/or...
whatweknow.inequality.cornell.edu