Is she cheating on me??(I'm hurt)?

God, where do i start? I got soo many Q&A on here about her.. I met this girl on a dating site a few mos ago. we seemed to hit off well. exchanged numbers, talked lots, emailed lots, and then eventually she moved in w/ me. the relationship was a bliss. a few weeks ago, I found out that she still logged onto this dating site, at first she was just checkin and deleting emails, until this guy. she responded to his email asking for a pic, he asks for an email, she gives email, he sends pic and she responds w/ "you're not so bad ur self" or ur cute. I simply asked her about this. she tells me that this is just something she did, had no explanation. i let it slide, no worries. we had problems, she sys it was because she wasnt used to being treated soo nice as I treated her. I mean she told me that she has been abused and misused, and etc. i had compion...ne way, she moves out bc she claims she needs to get on her feet(she ws styin w/ family when we met). I tried to convnce her that i