Is it normal to sleep on the floor next to your door

That's sad. Why don't you just get a lock or move your bed against the door? You need a good night's sleep to be refreshed the next day.

actually that's the best way to keep somebody from getting in your room unnoticed. Locks can be picked, alarm systems can be deactivated, or can give you false alarms. I suggest you also keep a gun or a knife or a sword within your reach. Alternatively, if you want to sleep on your bed, you can rig the door with either explosives or boobie traps. Like a big hammer meant to fall onto the intruder head as he opens the door and steps in. Like in that funny movie "home alone". But for god's sake make sure you remember to unrig the door and deactivate the boobie traps as well as the places you set them in. Or you risk blowing yourself up.
What's wrong with you?
What's wrong with them?!

You do sound traumatized. Perhaps, therapy or talking to a trusted friend could help you? You could get a lock or press something up against the door at night. It'll have to be heavy like a chest or a chair. I used to put my laundry basket against the door, but it was never really heavy enough:/ Even, a dog might help. If you have a dog, than it'll most likely bark if an intruder breaks in and it'll keep you safe.

I really feel for you...
Good Luck!

This is most likely due to your history with abuse but it is still not normal. Some options that might help, definitely see a therapist as stated before, but find other methods to make it very noticeable that the door will be opening. I would hesitate to block the door from being able to be opened from the outside simply because of fire hazards or emergencies where you might need to be reached, but instead find ways to make it loud to open your door so you can sleep in your bed. The best of luck to you.

Sounds like you're traumatized from your abusive ex. See a therapist, and get an alarm system or some sort of security system. Also maybe put your phone next to your bed while it's charging or whatever.