Are you asking about trill (carro /'ka.ro/) vs the flap (caro /'ka.ɾo/)? In Esperanto the letter “r” represents the phoneme /r/ (so the trill, like in Spanish carro or rosa) and not the flap /ɾ/. But it's sometimes realised (as in the majority of Indo-European languages, particulary in unstressed positions) as a single flap.
You won't find any good examples in English, where usually “r” corresponds to the approximant /ɹ/, rhoticity of the preceding vowel /◌˞/ or its length /◌ː/. In Usonian English you can sometimes hear the flap in words like butter ['bʌ.ɾɚ] or water ['wɔ.ɾɚ] and the trill sometimes in Scottish English, so that curd can be [kʌrd] (but now it's rather rare and more often one can hear the flap).
Most of the people you mention in your list should not have problems with the terms viro (“a man”) or virino (“a woman”).
Gays, lesbians and bisexuals are defined by their sexual preference (while still being males or females). Transsexuals identify and express themselves as the opposite gender than the one assigned at birth (thus in the end identifying as males or females).
Nonbinary people (such as agender and intersex persons), who do not view themselves either as a male or a female, are still people, so the word homo is the most appropriate, though an experimental term geviro (parallel to e.g. gepatro, gefrato and gefilo) may also be employed.
I see. I was just wandering because as a conlang I figured it wouldn't be held to the same binary restraints as regular languages. Many of the more modern words were created in this era to accommodate and I figured LGBT+ terms would as well find a niche where they could have equal weight.