Yes IF the developer supports it. You'll have to ask the developer whether they intend to do so.
Where did you hear this? Nothing in the official iCloud description indicates that app data is part of the cloud, only the app itself (http://www.apple.com/icloud/what-is.html).
Perhaps app data (and music streaming, etc.) will become features of the cloud, but there's been nothing official from Apple that I've seen indicating this.
It should work the same way document sync will for the iWork apps. The document store is part of the iCloud sync process. ANY app can take advantage of this if it's written using the proper APIs. This is why if you create and edit a document in Pages on your iPad, you'll be able to open it up and continue on your iPad, and presumably on your Mac as well.
Existing apps won't do this, of course. At least not until they are updated to take advantage of iCloud.
See this page: http://www.apple.com/icloud/features/documents.html
"If you have the same iCloud-enabled apps on more than one device, iCloud automatically keep your documents up to date across all your devices. So you don’t have to."
Things like saved games could be treated the same as any other document. The app just has to be "iCloud-enabled".