lostandhurt

Ask her out on a date.  No "lets hang out", ask her to dinner or drinks then dinner at a specific place and time.  If she says yes but then tries to invite other people or change it into a group thing simply tell her you want to spend time alone with her to get to know her better and that is really hard in a group setting.
See what she says. Basically ask for what you want and if you don't get it then you need to rethink spending any more time on this woman.
Lost

Exactly.
 She threw it all out there but was really uncomfortable about it so she left is my guess.
Don't try and be her therapist just be the guy she is dating.  Waiting to get a hold of her is probably making her think you don't want to date her any longer because of her past.  Call or text her and ask her out to dinner (in a restaurant) and see what she says.  Don't bring up her past or ask if she is okay or talk about her abrupt departure just have fun and leave her past where it belongs.
  Lost

Since everything looks to be above board here as far as him having the freedom to "date" this is pretty simple.
 He is into you from what you described. At first it wasn't a big deal when he was flirting so he was relaxed because there was nothing to lose but now that it is becoming real people tend to tighten up because they don't want to mess up an opportunity.
 Forget about the app and be brave.  You see him frequently so just ask him out on a date.  Make it clear you are asking him on a date though, no beating around the bush where he has to guess.
 "I think you are very handsome and interesting and would like to get to know you a lot better, would you like to get a drink and talk"    Or you can go the chicken long way around and use the app.
 Lost