I've noticed that there are some 2 or more player options on a lot of SNES and N64 games. Is this usable? So can more than one person play at the same time? If it is, then what are the keyboard configurations and/or how do you set it up? I know that you can change the keys by double-clicking the game, but this doesn't seem to work for many of them, at least for me. For example, I went on Pokémon Stadium  recently and tried double-clicking for the menu, but nothing happened.  

If 2 players are possible, I was thinking of connecting two keyboards to the computer so each player can have their own space (even if they need to hit different keys), and later, perhaps two SNES controllers when I purchase them in the future(not sure if this works out the same way though). Otherwise, using one keyboard can work as well, just not as comfortable.

It is possible. To do it, you just have to assign player 2 controls to the keys you want. However, I don't think connecting 2 keyboards will work unless you make sure that you don't use the same keys for both keyboards. So if player one is using the s key for anything, player 2 can't assign the s key for something or the action will happen to both players when either of you hit the s key. So just make sure no keys are being shared. That is if using 2 keyboards will even work. Most computers are set to only process 3-4 keys being pressed at once. So if both of you were moving down/right, you couldn't press anymore keys while doing this because they wouldn't be read. If your computer can process more than 4 keys being pressed at once, you might be able to play together. 

As for your Pokemon Stadium issue, if yo are using the Mupen64Plus, it won't work because it doesn't support 2 players and you can't configure the controls. I don't think the 1964 emulator can. I know the NES, SNES, and Genesis emulators can do 2 players.

IF you have a controller, you could do it where one person uses the controller, and the other uses the keyboard...honestly though this would work best with 2 controllers. You can get a decent USB controller to work with the RGR for like 20-30$ so they aren't too terribly expensive.