Maybe your bf should just totally ignore her and stop texting for her to go away. Block the girl's number, or even get a new number, and simply delete without reading any of her emails.
And you, my dear, stop being insecure. Your bf sounds like he loves you and is faithful to you and you alone. You need to stop checking his emails and texts behind his back - that's not trust - and without trust, your relationship will not work. So make it work - promise it to yourself and your bf - you will hold that urge to read his stuff and you will trust him. Think - what reasons has he given you to not trust him? Nothing. So know that you are being paranoid and you need to sort out your own problem - namely a problem of trust.
Either stop being paranoid and trust him, because a relationship without trust will never work - or break up with him, let the ex win and end your own misery.
I know that sounds harsh, but that's what I told myself last summer, when I was paranoid that my bf was gonna break up with me due to various reasons. And I told myself exactly that - either end your own misery and break up, or trust him and stop being paranoid. And since I was NOT gonna let pointless and unreasonable paranoia get in the way and destroy something that could be so good, I decided to trust him. And I got through it. I still have my moments - but overall, I'm over it now. Be strong - know that your boyfriend loves you - and there is nothing to worry about, because he loves YOU. It's you he loves, not her. Therefore it's you he wants, not her. And it doesn't matter how hard the ex tries, if he loves you, he will want you and you alone, not her. She can't wriggle her way back in because he doesn't want her and doesn't love her.
He loves you - there's nothing to worry about.

Be secure in your relationship and your love for each other.