You're right this is a debate sub. But most trans people don't take kindly to the comparisons you use, because they're often used to label trans people as mentally ill and in need of treatment, not rights. In addition of that they take a lot of effort to debunk, since they are so similar on a surface level. For schizophrenia you can look at the fact that there is a single case study of antpsychotics beeing used to "cure" a paitent of GID [Poland 1996] while there are multiple cases of schizophrenic trans people. interestingly these are mostly trans men, which is surprising given the spread of it in cis people.

The second is a pretty blatant false analogy. It ignores that trans age or whatever you want to call it is a new development without any precedent, I could find, before the 2010s. It's also not in any way medically documented in the same way gender dysphoria is.

Giving the benefit of the doubt I don't think you're arguing in bad faith, but you're using arguments that are often used to do so. Also the burden of proof is usually on the person claiming that something is. If you you say that these are comparable and are asked why you think so or are asked to proof it then you have to provide proof or, at the very least, your reasoning.