I had the same slow camera problem, it also sometimes opened with purple streaks.
Superhara below got me on the right track to fixing it. I had loads of apps open so this was slowing down the camera understandably, to close them all I double clicked the home button, then held the icons until a red circle with a white line through it appears on all the icons along the multitasking window along the bottom. Just tap this red circle to close all the apps. My camera opened quickly with no problems then.
I also noticed that when the camera is already open, if you try and open it on your home screen again it is slow to open, as it is already trying to open an open app. I got round this in 2 ways, either closing the camera fully when i finished (closing the app in the multitasking window by holding and tapping the red circle) or opening the camera from the multitasking window by double tapping the home button and selecting the icon here.
Hope this makes sense!
*** for the white arrow, is it the location setting turned on? an arrow comes up in mine when i have it activated. To turn it on/off go to settings, general, location settings.
Hope this helps!