It depends, do u really have feelings for this chick? Do you love her? If you do then stay with her. Become her babies daddy. It wouldn't matter if your not their biological father but if you love her then I'm pretty sure that your going to love her kids too. But hey you should follow your heart.
You should ask her why her past relationships didnt work out and get to know the women i know shes may have alot of baggage but everyone deserves to be love and if you can handle her past issues then power to you and if you love her stay with her dude its hard for single mothers so use protection with this women think smart if u ever get drunk make sure you put on protection before you drink if you end up doing something but dont get serious like kid serious with this women until u guys are married but just know you have options you could find a women who doesnt have alot of kids especially if your looking for a fresh start with someone.
that's honestly all up to personal opinion. do you trust her? why should you consider her past in your relationship? you weren't there when she was going through whatever happened. she doesn't want you to be a part of her past, she wants you to be a part of her future. and her future just so happens to be with three children that she has prior to your relationship and another child that she conceived prior to your relationship as well. so don't judge her on her past, because the more you judge her the more you are going to push her away, and if you really do care for her, she's going to leave when she gets to a point where she can't be pushed anymore.
It depends. Are you going to help her raise the children? Maybe she wants to find someone to settle down with, but she keeps finding people that will leave her. Be that difference and stay with her if she is worth the trouble