How to organize a local network of 15 laptops with group policy?

Question

Windows

There is an audience of 15 laptops connected to a local network using a wireless router.
14 laptops for students, one for the teacher.
On all Windows 7. Working group.
It is required to implement:
Prohibition on the launch (installation) of all programs, except for certain ones.
Prohibition to change the system time.
Deny access to system folders and important settings.
Shared folder for student assignments.
A student folder at each workplace for assignment results.
Is it possible to raise a domain based on windows 7?
Or just create reg files to quickly edit registry settings on each workspace?
I tried to configure the policy via mmc, but when I select a PC from the workgroup, I get access denied.

Answer 1

Nevertheless, with Samba on a virtual machine, it seems to me some kind of perversion.

Using samba as an active directory can be considered a perversion, but in a virtual machine this is a common thing. It is possible to raise a screw server with a domain in a virtual machine.
Or, as you yourself suggested, just create reg files for quick editing of registry settings on each workplace. Account with guest rights and go.