Should I go on a date with this girl despite all the problems?

I'm going to need lots of advice when it comes to this girl I'm talking to online:

1) She was just engaged in January to someone and they broke off the engagement last month and she is still friends with the guy on social media

2.) Me and her were getting to know each other through messages a couple weeks ago when she told me she just wants to be friends since she was seeing someone. But yesterday she said she's interested in dating me because the guy she was currently seeing wanted nothing to do with her after one date and she got really depressed. I don't know what signals she is sending because I went from "just friends" to "wants to date me" in a matter of a week

3.) And she has a different last name than her Facebook last name when researching her to see if she's worth dating. I don't know if she using a different profile to talk to other guys. 

Is she worth going on a date with? I don't know why I always question if it's worth going on a date with someone online when I get the opportunity.