Not only possible but also recommended..
As for save files, that depends on the game, usually in Documents or game folder.

Just so you realize: you will only be copying the installer on the external disc: the game still has to be installed and played from the HD, and that's where the save file will be located.

If you want to have a portable version of the game on a disc, then it's a different matter altogether, and for some games not possible.

Are you sure? I already tried downloading the game, put it on the disc, then I unistalled it from the PC, and the game still worked, saved and loaded from the disc.

For some games this works, for other is a bit more complicated or sometimes, like ZFR already mentioned, not possible.

You should also keep in mind, if the game keeps saves in the game folder, you will be not able to save at all.

Depends on the game. Some will run (and will keep saves on HD). Some might run but with problems: e.g. you might not be able to save your game, or your settings. Some won't run at all.

You can put them on any storage medium providing it has sufficient space.

Can I just copy all files to multiple disk
Then move to new computer in a folder say called
mdx and run game
Isn't that what you do when you install a
game with two or more disk

The thing is, when you install a game it may do a little bit more than copying files to one location. Wouldn't it be more convenient to download an installer and install the game on another computer? And would it be much more convenient to use a USB flash drive instead of burning files on optical discs?

I guess it depends on whether they own a USB flash drive large enough to hold said game they wish to transfer ?, as some game installers can be as much as 100 GB's. They may already have a vast collection of blank DVD-R/W disc's in their possession collecting dust ?. A large reel of DVD's holds 100 disc's, so that's over 400 GB's of space right there... ;-)

You didn't burn the installer then, but the installed game.
A installer looks like this:

setup_x-morph_defense_complete_edition_1.0.0_(64bit)_(27014).exe
setup_x-morph_defense_complete_edition_1.0.0_(64bit)_(27014)-1.bin
setup_x-morph_defense_complete_edition_1.0.0_(64bit)_(27014)-2.bin

Using this .exe you can't play the game directly.


ps:
About putting a installed game on disc .... that might not be the best idea.
Games which are small enough to actually fit a disc are usually also old. And old games tend to write their configuration files in a file that lies in the game installation directory. That's a serious nono these days, but 20 years ago sadly many did it this way, some games even put the savegame data there.
If you have the configuration file or savegames on a non rewritable device you won't be able to change it (and that's why it's a nono. Games which do that and are installed into the programs directory need admin rights to write their config files)