Hello EvaT,
The greencard stuff I have no idea, but he does this immigration attorney has info. on there that maybe relatable to you, the citizenship stuff I do know, please read below, its my personal short narrative.
YMMV, meaning everybody is different.
I ended up getting my US citizenship in 2003, due to my USMC time during a war period(Persian Gulf Era/1991), but as a man. It makes it easier to explain your original gender in the USMC, than adding another wrench into the system(change of gender) and really confusing the Homeland Security/Citizenship and Immigration Services people(CIS), They will more than likely not understand, by lip services yes, but really deep down inside, nope. If your a veteran during a time of war, since you look kind of young in your pic, you may have served during the GWOT period, even if you never set foot in the sandbox, as long as you were in, during the GWOT/Persian Gulf era. INS/CIS doubted my time in mother corps, since I just don't look the jardhead type, I just rather have my attorneys handle this rather delicate situation. Don't know what part of the country your in, but you can get free info. on Carl Shusterman's website. Just for info., pretty sure the federal laws are same nationwide. The greencard stuff, I have no idea.
No I'm not a representative or being compensated by him or his affiliates, he helpd me out pre hrt in my 30's, in my man days.
https://www.shusterman.com/naturalization-through-military-service/Naturalization Through Military Service Immigrants who have served in the US Armed Forces during a time of hostilities are eligible for expedited naturalization.
Those who served honorably since September 11, 2001 are eligible to immediately apply for naturalization. This is also true for those who served honorably in a prior conflict (World War II, Korean War, Vietnam War, Gulf War, etc.)
There is no requirement that an applicant for naturalization through military service during wartime have any period of continuous residency or physical presence in the US.
Applicants must be persons of good moral character, know English, and pass a US history/government test. In addition, they must take an oath of allegiance to the US.
They must submit a Form N-400 Application for Naturalization, as well as forms verifying their military service.
Naturalization through military service during peacetime requires a minimum period of 3 years of permanent residence in the US. The applicant must be physically present in the US for over 50% of the past 3 years.