It's better for her to get the visa and move to the US while you are still outside the US without a GC, so she can cleanly stay away from mentioning you.
I don't believe they ask who the student will stay with, they just ask for the address. Although it's possible they could ask about the "who" in the interview, if it's not a campus address. Living with you the GC holder would likely be a problem for them. Saying she'll live with your stepmother shouldn't be a problem while you're still outside the US. Although she should just say she'll be living with "a family friend" instead of "my boyfriend's stepmother" if asked about the relationship between her and the person she would stay with, and they probably won't dig deeper for more specifics.
The time to answer those questions is in the GC interview, which is at the very last step of the process. By that time she would have finished her studies and either be back in the UK interviewing at the consulate, or inside the US working on H1B, so either way you won't be bothered with immigrant intent questions, and you can freely admit you were already dating back in the UK ... as long as that doesn't contradict what was said earlier in the visa interview or at the port of entry.
Basically, you want to coordinate the sequence of events (her F1, your GC, etc.) so that she's not in a position where she might have to answer questions when applying for her F1 or using her F1 that would put her in a position where she gets refused entry for telling the truth or tells a lie and gets screwed later when the lie is caught.
So initially when applying for the F1 and using it for the first time, if you're not married or engaged she won't have to list you on the application. If they ask "do you have a boyfriend", she can truthfully say "yes and he lives in the UK".
Then while she's studying and wanting to travel outside the US between semesters or spring break, they're unlikely to ask relationship questions at the airport or border. But in the 5% chance that they specifically ask if she has a boyfriend she can honestly say Yes because a large percentage of college students have boyfriends or girlfriends but most of them don't end up marrying that person. And if they dig further and ask if she's going to marry her boyfriend, she can truthfully say "I don't know, I'm not marrying anybody before I graduate". Just make sure you don't raise the officer's suspicion level by crossing the border or approaching the immigration counter together with her.