Your all infatuated by her. Its completely normal in the beginning to feel jealous, anxious, paranoid etc You just need to try to relax. What is the worst thing that could happen? She cheats and you break up, you take the time to get over her, you heal and move on with your life.. That is all there is to it.
It takes time to build trust-just dont tell her that you are having all these thoughts as there is nothing less attractive than a jealous bf/gf.
It is important to have boundaries: example if she has a very close male friend who she wants to hug and text and spend time with alone-that should be a deal breaker-you end the relationship because of that. Another example: if she acts like she is single and flirts with other guys you break up. If she cheats-you break up.
As long as you know what your boundaries are and what you will or wont tolerate then you will be fine. Same rules should apply to both of you obviously.
If you want to have a discussion with her about trust and boundaries-go ahead. But make sure you dont use an accusatory tone. Example: trust is very important to, I feel a relationship is nothing without it and I always want us both to be honest with each other no matter what happens.
"Don't ask a question if you can't handle the answer".