Some words for sexual orientations:

* sexual orientation = drawing or faining (fain is an archaic English word for desire; see https://www.merriam-webster.com/dictionary/fain )
* #asexual = undrawn or unfaining
* bisexual = twain-drawn or twain-fain
* gay (in the sense of homosexual) = same-drawn or same-fain
* gay (strictly in the sense of men loving men) = wer-drawn or wer-fain (wer or were is an archaic English word for a specifically male human, whereas "man" was a gender-neutral word for a human; see https://en.wiktionary.org/wiki/wer#English )
* heterosexual = other-fain, else-fain, or else-drawn
* lesbian = lass-fain, lass-drawn, lady-fain, lady-drawn, or wif-fain (wif is a Middle English word for woman; see https://en.wiktionary.org/wiki/wif#Middle_English )

Some words about gender:

* gender = kind
* assigned gender = allotted kind
* gender dysphoria = kind-woe
* #transgender = cross-kind
* transition = crossing
* cisgender = same-side-kind or stay-kind

Some words about nonbinary gender:

* gender binary = kind twofoldness
* binary genders = twain kinds
* #nonbinary = untwain
* genderfluid = kind-flow
* genderqueer = kind-queer
agender or genderless = kindless
* bigender = twi-kind
* neutral gender = fair-kind
* neutrois = fair-three

Building words from Germanic English roots is a fun linguistic experiment that is helpful when you find yourself overwhelmed with what we think of as "long words," which are of Greek or Latin origin. Wikipedia gives several examples of writings that attempted to do that:
https://en.wikipedia.org/wiki/Linguistic_purism_in_English
The #Anglish wiki has a lot of resources for if you want to try it too:
https://anglish.fandom.com/wiki/Main_leaf