What you can do is give the workgroup name at home the same name as the domain at work, and create a local account on the laptop that is the same as your domain user account. When you logon to the domain on the LAN, the PC stores your logon details. When disconnected from the LAN, you can still logon to the domain, though your logon is effectively local. You should still have access to workgroup resources because the domain/workgroup and usernames/passwords are the same.
Be default, any user can add upto 10 devices to the domain. Administrators may have fiddled with this though. Not aware of anything preventing a user from removing a machine from the domain though
Administrators can only add 10 devices to the domain. To add more requires Account Operator rights. The default location for a machine account is the "Computers" OU, but most administrators, especially those that have power insecurities, like to create different folders for different types of computers - so different GPOs can be applied. Re-adding a PC to the domain would put the PC in the Computers OU, thus upsetting the administrator's schema - resulting in a tantrum.