Can a sex change be covered by health insurance if gender identity disorder is proven?

Depends on benefits. This will depend in the unique benefits of each plan. I would contact your plan administrator to ascertain your level of benefit coverage.
Yes to may cover. As vp joe biden said recently, referring to equality for transgender -identified persons, "this is the civil rights issue of our time." increasingly, health insurers are covering gender-affirming medical interventions. Those of us who advocate for trans-inclusion & equality view these treatments on par w/ treatments for medical conditions" like pregnancy. No one would say pregnancy is a disorder!
Difficult to answer. There are few insurances that will cover the total or even major portions of a sex change procedure from start to finish. There're various organizations and grants that can help. Google " glbt, lgbt, algbtic, lgbtco" for more information. There are ways for you to succeed.
Yes, in many cases. Whether Gender medications, therapy, and/or surgery are covered may depend on your policy. Many large companies (Microsoft, Google, Amazon, etc.) do cover transgender care. Some cities cover it for their employees, i.e., Seattle, San Francisco. And a number of universities cover it for students covered on student insurance. Many policies say they cover it, but are still hammering out the details.