tbh Im not quite familiar with Galka, don't know much about her personality beyond her being a cop to answer this questions...I might replay the game soon to get more info about her and give a proper answer, but meanwhile I will answer anyways making wild guesses on her personality and maybe memeing a little bit
Well since the orc girl already embaces the archetype of delicate/sweet giant, I want Galka to go a different path, now which personalities fit her better without being too cliché?
I can think on two possible paths
1.- A disciplined brutish Galko, I want her to be kinda like a samurai, she is big, strong, confident and the kind of person that doesn't mind using her strength to solve most problems, but also she is very disciplined and always willing to follow orders, I envision the Goliath race as a highly hierarchical society and one were discipline is enforced from young age and she is both prepared to kill and die for her superior, kinda like a rough and brutish, but honest and loyal companion.
2.- A frustrated dom Galko, Im not even joking, hear me out
!. She comes from a highly hierarchical society but she always has been...lower class, that means she was forced all her life to follow orders and she had little opportunity to climb her social ladder on her world, that's why she shows respect to her superiors, but she inside lives in frustration because she really wants to be the one in charge, be the one that gives orders and want people eager to please her, she is both cunning and ambitious and plans to climb the social ladder on the human world since she didn't had a change in her world in order to be in a position of power over others, not because she is evil or wants to humilliate others, but because she wants to be praised and admired.
what would you do?
in both cases the answer is simple, TRAINING, Galka is strong, like super humanly strong, she might not have Auron's martial prowess, but she knows how to take and give a hit. That's why she will help Auron learn to deal with opponents several times stronger than him, since he only trained with other humans he needs to adapt his style to deal with attacks he can't possibly block and will spend several days training with Galka to become a better fighter (for plot reasons).
What would you ask her, and what would she ask you?
I would ask her to step on me Auron should be always curious about Goliath society and biology, since us players know nothing about that either it could be a cool way to expand the lore of the world, and of course eventually asking more personal questions about her family and people important to her as they get to know each other better.
She on the other hand would ask different questions depending on her personality. if she is a disciplined brute she would would be very direct and ask a lot of very personal questions from the get go, like dick size and that kind of stuff. Dom Galka would be more interested on using the leverage on the fact she teaching you to make you do stuff for her even sexual stuff, we could use more sexually dominant females on this story.
What parts of the campus would you hang out in, and what kinds of things would you share?
I don't know if in the campus, but in general I believe they should train in Auron's house, and hang out maybe on the security office.
Would you visit any other characters with her along? If so, whom would you visit, and what would you talk about?
Of course, the more the merrier.
brutish Galka would bring the elf girl and the Muai Tai girl the elf girl will be there to heal you if things go bad during training and the Muai Thai girl (I know I suck at remembering names XD) will be training with Galka along side you since she wants revenge after her initial loss (though she wouldn't mind being overpowered again)
Dom Galka would probably not be interested in bringing people but of course anybody can tag along.
Would you reveal any secrets to her? Ask her help with something?
Sure, in my head canon she would be helping Auron to learn to deal with overwhelmingly bigger and stronger opponents, but also since she is a cop, she will probably help Auron find the yandere girl, now I think Auron has no reason to disrust her and I don't think he would have problems sharing his secrets with her.
For those of you who like larger species, how would you go about catching her interest?
As with any person, if you talk with them, and show affection you would probably catch their interest. Now in the particular case of Galka, with Brutish Galka if you demonstrate commitment and take your training seriously, she will respect that and show more interest. Now with the Dom Galka, of course being willing to partake in some light femdom and if you decide to help her earn merits in order to get a promotion she will be delighted to have you as a partner.