If she's separated instead of actually divorced, that's a sticky situation. Especially if she's already had her estranged spouse threaten to kill her. Considering that, you might give her time to get fully divorced. If he is a violent nut, you could be at risk if you began dating her.

When the time's right, dating sounds harmless enough. But be very careful about getting serious. A young woman with three kids is very likely looking for another husband to help her raise and support them. A built-in family like that is a huge responsibility for someone who's just in college or just about to finish. You might also note that she's clearly pretty fertile, so use birth control!