I think your friends' advice holds some water here.
Don't go heading into a rescue mission relationship, especially when you've already decided against it once before.
I can personally tell you that 'raising' step children is one of the most difficult things a man can do. On the 'good' side your friend's daughter is young on the bad side she is your friend's daughter, not yours. Even if things get to the point where you marry her she will still not be your daughter. You have no standing legally or otherwise with that child, discipline is her mother's baliwick, and you can expect that if it come to supporting you or backing you with that child you may be left out in the cold.
Not unless the father gives up his parental rights and you then adopt the child. In your situation I would seriously advise against this unless or until you and the mother are married. If you do this before and you don't get married then your, and her, ability to relocate is seriously compromised and with your job situation that ain't a good thing.
Try to put any emotional response out of your decision-making process for a moment. Don't get caught up in fantasies of "what could be" with this woman you haven't had a functional, healthy relationship with and who has a child you don't know whether you would truly have a bond with. Being in your late 20s isn't that old. You have plenty of time to find the right person to settle down and start a family with. She may or may not be The One.
It sounds like she's clinging to you to get out of a bad situation; she may not realize it on a conscious level, but she is looking for help not love right now. If the woman can make her way back to the US and get established on her own, great; don't be her lifeline/rescuer.
Is either the biological father or the child a German citizen? If so, you may fight yourself in the middle of a nasty international custody fight.
I'd also be wary of someone who would leave one relationship (even a crappy one) for another.
There are lots of things about this situation that are sketchy (cue the robot from "Lost in Space" screaming, "Danger, Will Robinson! Danger!")
That should say, "If so, you may *find* yourself in the middle of a nasty international custody fight."
I was about to call you pedantic. But then I saw you were correcting yourself.
Yeah, I wouldn't be that much of a jerk to someone else.