You can't find a Golden Chocobo, you have to breed it. The process is time consuming and exhausting, so prepare yourself for hours of birds mating and races (because you have to train them too).
The complete process can be found in this guide explained quite in detail.
To sum it up you have to:
- Get two good yellow chocobos
- Train them to class A in the golden saucer
- make them breed and get a Blue and Green chocobo (they have to be of different gender)
- make them breed and get a black chochobo
- train it to class S
- make it breed with a class A chocobo
- finally obtain a Golden chocobo
Inbetween you'll have to find various objects to feed to your chocobos, and various things are completely random (such as the gender of the chocobo you'll get). Be patient and your reward will come!
Oh, and obviously you can use it in the Golden Saucer, it's simply the best Chocobo you can get. It can also cross any terrain on the map, including water.
Another way to get a Golden Chocobo that I just discovered is to get the Desert Rose, the reward from the Ruby Weapon, to the Kalm Traveler. Depending on your group and skills, this way could be less painful.
No.
Element materia linked to a materia with element type only gives you a damage multiplier against monsters with elemental affinities.
If the monster is weak against the linked materia, you do 2x dmg.
If the enemies are resistant to the element, your attack can do either half dmg, no dmg, or heal the enemy.
From what I can remember and what I have found through searches, the damage provided by the combination does not scale with either the level of the Element materia or the materia it is paired with.
Best Answer
The Cave of Gi on Disk One is the only place to get the Added Effect materia. If you miss it, sold it, or otherwise got rid of it, there is no way to get another.
See here for more information.
There are unsupported rumors that you are able to dig one up in Bone Village at a later time, but I've never seen conclusive evidence that that's the case. No reputable sources on the web support that claim.