The common shell variables differ according to which shell you are talking about. In general, they control the shell environment behavior, terminal behavior, and other external things.
You can get a list per shell by using the 'man' command with the shell name to list out the common variables used in that shell environment.
The mini shell program is used in Unix as a programming software. It is a redirected and streamlined approach at creating variables, commands, and tokens.
There is no "default" Unix shell. Different Unix vendors shipped different shells.
The first shell was 'sh', the Bourne Shell
A Unix shell can be obtained in Cygwin, a Unix compatibility layer used to compile Unix programs and run them on Windows. Microsoft also makes a shell known as "Windows PowerShell" which incorporates more Unix-like features than the standard command prompt.
The a default Unix shell is the shell that comes with and is activated initially with your distribution of Unix. The shell is essentially the program the runs the command line interface allowing someone to interact with their computer. Some examples are the Bourne-Again shell (bash) or the Bourne shell (sh).
The Korn shell.
For windows, you might use .cmd, .bat as common file extensions. Unix doesn't use file extensions as associations, so no file extension needs to be used in the Unix environment. A shell script in Unix is simply a text file with any name that is readable and executable. However, file extensions are typically used in Unix as a documentation aid that states that the file is a shell script. Common extensions are .sh, .csh, .ksh, .tcsh, .zsh, etc.
The Z shell is a Bourne-compatible shell for Linux and Unix systems.
You should be able to download the Unix Services for Windows, version 3.5, from Microsoft (free). There are other shell emulators that are available for Windows, which would allow you to use Unix type shell scripting without installing any additional OS. Your question about "virtual UNIX" is unclear ..
Environment Variables: Sometimes called special shell variables, keyword variables, predefined shell variables, or standard shell variables, they are used to tailor the operating environment to suit your needs. Examples include PATH, TERM, HOME, and MAIL.User-defined Variables: These are variables that you create yourself.Positional Parameters: These are used by the shell to store the values of command-line arguments
shell
The bash (short for Bourne Again Shell) is a popular command shell for Linux and Unix-like systems. It's name comes from the Bourne Shell, an old shell found on many older Unix systems. bash is a free reimplementation of that shell.