Ohhh.
So Lora saw a Cruxi Leader trying to talk to her. Interesting. He was probably saying something like, "ayy lmao baby, want some fuck?"
Uh no. That was my character Mai -_____-' *sweatdrop*
And really, depending on which team she's on, Mai can be either a help or perhaps a hinderance. As far as I know, 74% sync on Mai's part is the lowest out of all the pilots. The only thing she has going for her is that she's...well a "trained killer" of sorts from the previous framework division she comes from so mentally, she's the least likely to brain freeze when the bullets start flying. Plus, I'd imagine she's better trained with the Starfist but again, her low sync will keep her from moving at the speed she wants. Then of course, there's the unknown factor with her "seeing future events" thing.
In regards to her relations to the other pilots over that two month period, I think the only problem she'd have will be with Yeshua as Ariamis put it. Someone who's always THAT happy would make even Mai feel arkward. Everyone else, I think she'd either trained or studied with when they requested to do so. Just that Mai isn't a talkative type. Though I think they could be "moments" that Mai could have with the pilots that showed that, due to her speaking her mind to Lorenzo and Ritsu, that she's still human deep down despite her training making her like a "robot".
I thought of one instance that perhaps Elora, upset with the situations she thinks she caused, approaches Mai at one point and asks her to train her on how to be like her. Mai, of all things, would refuse, stating "that life style would mentally drive you to death" and "stop crying. At least your still human. I'm not." I don't know about these exact lines but I thought this moment could have happened.