I'm not sure what you mean by pull out menus.. but any icon on the homescreens you can move around as you see fit. Just tap and hold the icon / widget till the phone vibrates then move it around as you see fit.. or drag it to the bottom to remove it entirely.
No, if the phone is turned off the alarm will not go off. However if the screen is off and the phone is sleeping it will wake up and sound the alarm. Just be sure that the alarm volume is turned up, you can do this by going to where you select your alarm sound and hit the volume rocker up. The Phone's ringer volume and alarm volume are two different settings.
