Can hormone imbalance cause gender dysphoria?
That isn’t likely. Hormones don’t cause our internal sense of gender – that’s something that is innate (built into us). A person who doesn’t otherwise have gender dysphoria is unlikely to develop it solely because of a change in the hormone levels in the bloodstream.
If hormones shift enough where a person were to develop secondary sex characteristics which were incongruous with their experienced gender, they might develop a form of gender dysphoria — if they (and/or others) begin to perceive their body as belonging to someone of a different gender. But that isn’t the hormones directly causing the dysphoria, but the effects of the hormones on the body (and on people’s perceptions of that body).
Hormones can influence how a person with gender dysphoria experiences that dysphoria. My own gender dysphoria was worse when the hormones my body naturally produced were allowed to flow without any controls. By bringing those hormones under control and shifting the balance of hormones to align better with my experienced gender, my gender dysphoria improved significantly.
Do you think a traumatic past might be the reason for some people to identify as a gender other than their birth gender? Why or why not?
This has been studied and found that there’s no link. The causes for people being transgender aren’t yet known (and may never be), but we do know what they are not — trans people aren’t “so gay that they modify their bodies to attract cisgender people”, and aren’t “people who have been traumatized so badly that they reject their assigned gender”. I’m living proof of both of these – I’m a lesbian (so was never into guys), and was never sexually or physically traumatized. The only trauma I’ve suffered is from how I’ve been treated because I am trans – which logically could not be the cause for me being trans!
All that said, I’ve been struck by how many trans people I’ve met who have suffered physical/sexual trauma in their lives. In nearly every case, the trauma came after they knew they were trans (or at least knew they weren’t cisgender). It’s almost as though some people see transgender people as targets for their bad behavior! (FYI, that was sarcastic – there are people who totally target trans people for their bad behavior!)
The reality is that we don’t know why some people are transgender, but that doesn’t make the experience any less valid.
Is there a connection between low testosterone and transgender (MTF) women?
Nope. My testosterone levels were at the very high end of typical male levels, yet here I am, transgender woman.
Gender World 
My childhood included having a religious zealot of an abusive mother, then going through a horrible relationship and being on the edge of suicide over and over. The day I shaved off my body hair and rejected everything that was male and painful changed everything. When I changed my name and got rid of everything male in my home everything fell into place and the more I went with my feminine side the better I felt. I cant even imagine going back to those days.
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