False a transgender person is anybody who identifies as transgender. I say this because some people that typically fall under the transgender umbrella don't identify as transgender.
Transgender can include people who are intersex, transsexual, androgyne, agender, bigender, genderqueer, drag kings, drag queens, genderfluid, gender ->-bleeped-<-, two spirit, queer sex, pangender, two-spirit, third gender, hijra, trigender...and that's all I can think of.
Also false that gender is a spectrum. A spectrum is very much point A to point B where gender is multi dimensional.