Should go i break it off with my girl friend?

Welll me and my girlfirend i have just started dating but before we went together i asked her what has she ually did so i got these answers : pleasured a man(oral) made out with a woman, getting fingered. Now i know it might be shallow but i can get over the last two but not the first cuz i dont wanan kiss no girl who suck some other guys ... And Recently after few weeks of going together her ex who she hasnt heard from in 2 years txt her...They didnt break up by cheating or anything but they became distant by not communicating,..She tells me she wont get with him and thats she almost over him(which i doubt) So then she told me another ex called her parents for a date with her...She says she has no choice..and she has to go and im jealous at the idea that an a hole like him did that..She hasnt went on the date yet cuz there is no set time yet but later on the next day she told me she was at her moms job and that her mom tricked her into a date with some middle school friend..Her parents dont know that i go with her yet and she told me that if anyone wants to go on a date with her they have to call her parents...so i asked and she said no cuz she doesnt like dates...but she just went on one?....Inside i dont feel comfortable with all this should i break up with her