Yes, non-rotation of homescreens is normal.
The appdrawer comes up when you tap on the icon "Apps" in the lower right had corner of the screen--it's just the list of all of your apps, which can be customized by adding custom drawers (e.g., "Games" or "Travel"). You can then put a shortcut to your custom drawer on a homescreen, which I find avoids the slowdown that can happen if you create folders on the homescreens instead.
If you open the appdrawer, that screen will rotate when you move the phone around.