Not all doors can be entered. At least from what I played.
Regarding the speed, my perception is that the "fast" is what should the normal and that the extra fast is way too fast.
Viewing post in Scream Mr.Jack - MD jam comments
The doors that can be entered have some pointers cause not all doors can be entered and those that you can change from time to time.
I personally cannot read as fast as the double speed. The whole idea was that you use double speed to speed forward if you just want to get to the next line of text and quadruple when you need something like a skip. Skip cannot exist cause the game is in real-time.