Prevent users from installing software, altering desktop (files, icons, &wallpaper), changing Start menu

I've read several Q&A here that each address one of these restrictions, but found none addressing several or all of them together.

Context: Windows XP PCs in teaching labs have two accounts, one with administrator privileges (and a good password, students don't use it) and one with regular user privileges used by all students.

In XP the regular user may:

1. install software in their account
2. put files on the desktop
3. move Desktop icons around
4. change the desktop wallpaper
5. change the Programs submenu of the Start menu

I'd like to prevent all these (especially 1, 2, and 3, they usually don't do 4 nor 5). Students must:

1. ask the admin if they need new software
2. put their files in a subdirectory of My Documents
3. 4. 5. not impose their taste on other users

I'm looking for a unified way to accomplish all these. I've read about something called "group policies" that may be the way to go:

• do you confirm it is?
• can you tell me the procedure?
• will this work the same in Windows 7?