Is it abnormal to be this paranoid?
You're not paranoid. You have good reason to be concerned. This world isn't safe for any woman. (I'm gonna get flamed for that, I know, but I stand by it).
Have you considered owning a firearm and learning how to use it, if necessary? That could really give you an advantage if you need to defend your life in your own home.
Good locks are important. They're only effective if you use them all the time
. I can't tell you how many people in my community have become crime victims because the criminal entered through an unlocked door.
I'm glad you're thinking about this now, before the worst happens.