I don't think so, because Yellow is first generation, and Gold is 2nd.
They can link together, but in a limited access as Yellow doesn't have all the Pokemon in Gold.
You might have more functionality if you completed the game or catched all the Pokemon in your pokedex, but I'm not 100% sure.
Yes you can trade Pokémon between two Pokémon Yellow games.
You can't
Yes!
yes
in Pokemon yellow there is no Pokemon stadium
Luckily for you bilinguals (I am too :]) yes
Yes it can. Using the Time Capsule in Gold and Silver it's possible to trade between Red, Blue, and Yellow.
Yes you can, if you own a link cable to connect the two gameboys.
on Pokemon yellow on Pokemon yellow
No. They were made after Pokemon Yellow.
There is no Pokemon Spark Yellow game.
No, you cannot get Lugia on Pokemon Yellow.