They only go back to the same spot if there is no room for the icon to move. You should have at least one empty spot to move things around. delete one or move it to one of the other screens temporarly.
Hold down and then move the icon where you want then move the last icon back.
If you mean the screen you slide up which holds a list of all applications, then no, that can't be re-arranged. Perhaps in one of the home alternatives, but I doubt it. Haven't tried any so I am not sure.
I dont think there is a way to rearrange the icons on the application screen, and as you add new apps, they are going into alphabetical order - so they are in different places all the time.
What I did was add folders to the home screen to hold groups of apps in ways I was used to looking at them - direct dials, games, utilities, apps.