You have 5 slots. If you do not pause the game before you either quit the program or switch to a different slot, the game continues to "run."

For example, if you have 5 games, one in each slot, and none of them are paused, and if you quit the game and turn off the computer at night, when you turn the computer back on the next day and run VV, all 5 of your games will have advanced.

I am not certain about your key working on your other computer. If you bought the game from BFG I can tell you with almost 100% certainty that your key will not work. BFG will however give you up to 4 more keys to install your program 4 more times. These installs can be used on your other computer. They are intended however to let you install the game on your own computer if you either upgrade to a better computer or if you are recovering from a system crash where you lost your hard drive.

Lastly, if you are petrified of doing anything because you will lose your tech points and love your villagers, you can just make a backup of the game save files. In fact that is a good idea to do that for everyone anyway.

You can search the forums and you should be able to find threads that tell you how to backup the game save files.