She knows how painful it is, and would never inflict that on another person.
You're super-suspicious of everything your new partner is doing, and you don't know if you'll ever trust someone again.
Look, it's not your fault that her last guy was an treated her bad but you're going to have to work a little harder and follow through on whatever you say with actions, so she knows she can really trust you.
Just give her some time, once she trusts you and you're consistent with what you do and say, you're golden.
If your new girl was burned in the past, she never wants to feel that pain again. And chances are she's going to be looking for warning signs up front. So be honest with her and you'll earn her trust. See point number one.
She can't help it, she's a bit insecure because of what the last guy did to her, but can you blame her? Bottom line: If you're not that into her or not "ready to be with someone right now," don't lead her on.
Just like she's going to ask you who you're texting occasionally. But this is a fair and totally normal question to ask if you're going to be in a relationship with her unless you're up to something shady, in which case she'll dump you like that *snaps fingers*.
You know how people's minds work: Before you can even explain what happened, she'll think you're dating one of them and have cheated on her 11 times. That's just where her mind goes until you earn her trust.