Romantic-wise if you are romantically attracted to the same gender then that’d make you homoromantic, as you say. (You could also consider the term panromantic - since your romantic attraction isn’t dependent on genitalia and so a little broader than being strictly homoromantic).
Asexuality is all about not finding others sexually attractive and is unrelated to sex drive/arousal and masturbation - so experiencing any of those things doesn’t mean you aren’t asexual (also not experiencing them doesn’t mean you aren’t ace either!).
Grey-as experience sexual attraction infrequently and so still regard themselves as on the asexual spectrum.
Some asexuals are comfortable to have sex (etc) with their partners, and even enjoy giving/receiving, whereas others are indifferent or completely uncomfortable and repulsed.
Hope that helps!