You asked me three questions. Before I answer any of them, we have to talk.
First of all, both you and your girlfriend are drowning in jealousy--and it sounds like with good reason. She fears that something is going on behind her back, and it turns out you cheated on her even before you set up the 'New Deal. 'So, she had reasons to mistrust.
You were jealous of her constant flirting. And, you had reasons to mistrust her because now she is seeing two other guys. There are too many unknown variables here.
For starters: why are you both flirting and cheating? Both of you seem terrified of becoming close with another person. Behind the flirting and cheating often lies the fear of closeness; and the behind the fear of closeness often lurks the fear of abandonment. (If I let you close to me and you dump me, I'll be destroyed. )
Both of you seem be be trying to get a jump on the storm: I'll cheat on her before she cheats on me. I'll flirt with and date other guys before he has a chance to dump me. Both of you decided to open the relationship to other people. What were you hoping to solve by doing this? By diluting the relationship in this way, it feels like you are both escaping the real issue.
Why are you both so terrified and mistrustful of love? To answer this question, you need to do some emotional homework and find out where these insecurities originate. Both of you have been hurt and don't trust love. You need to figure out where these hurts stem from and talk about these fears with each other.
In answer to your first question, can your girlfriend truly love you, yes she can love you, but if you don't deal with these fears of closeness, the love may become buried by unresolved emotional issues.
Secondly, in answer to the question, is seeing other people more destructive than helpful, if you both are dating others in order to avoid intimacy, I think you begin to see that by doing so you are not solving the real issues. Also, by dating other people, there is the risk that the abandonment fears and jealousy reactions will become more intense.
So, my advice to you is that you both do your emotional homework, and together face and discuss your fears of closeness. I wish you luck. Let me know how it turns out.