To start with your second question, it's kind of up to you. If you wish to, you can continue to follow the Objective-C convention of having one class per file, although this isn't a requirement, and wasn't in Objective-C either. That being said, if you have a couple of classes that are tightly related, but aren't made up of much code, it wouldn't be unreasonable to have them grouped in a single file. Just do what feels right, and don't make a huge blob of code in a single file.
Then for your first questions... Yes, you had a good deal of it already. Basically, from where you got up to, you need to create the instance of GameScene through its size: initializer. From there, you just set the properties and call present.
override func touchesBegan(touches: Set<UITouch>, withEvent event: UIEvent?) {
super.touchesBegan(touches, withEvent: event)
guard let location = touches.first?.locationInNode(self),
let scene = scene,
nodeAtPoint(location) == "Game Button" else {
return
}
let transition = SKTransition.reveal(
with: .down,
duration: 1.0
)
let nextScene = GameScene(size: scene.size)
nextScene.scaleMode = .aspectFill
scene.view?.presentScene(nextScene, transition: transition)
}
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