Question: Is it possible to install/register another local server instance in any SqlServer version, besides the default local instance, where only one SqlServer version is installed?

Answer: 
Yes, it's possible. I have several combinations in my servers. I have one server that has both SQL Server 2000 and 2005 installed side by side. My desktop at work is a Windows 2003 Server, and I have SQL Server 2005 and 2008 installed side by side.

What you want is called a named instance. There will be a screen during the install, where you will be able to give it a name.
Yes. Usually the installer will detect that you have one or more existing instances and will prompt you for a instance name. We have setup three SQL Server 2000 standard editions on a development box to emulate the three production servers at one of our clients.