1. Will Swift be cross-platform or is it going to be strictly for MacOS X and iOS app development?
2. Will Swift apps run on older versions of OS X and iOS? I've seen differing opinions (e.g., http://stackoverflow.com/questions/24001778/do-swift-based-a...)
However, it doesn't have much of a standard library as part of the language itself at the moment, being heavily dependent on Cocoa stuff. GNUStep/Cocotron could presumably be used.
2) Yes; Swift apps run on iOS 7 and up, and MacOS 10.9 and up. There currently seem to be some bugs which turn up on iOS7 but not 8 or vice versa, but Swift is quite buggy in general at the moment, and this will probably be cleaned up.
It would make it a no brainer language to use for a mobile app, because you could kill two birds with one stone. To date however, apple has made no comment about cross platform development
Knowing apple, I feel that they would have an off the shelf solution that you could just push code to. Almost like a parse type solution, integrated through Xcode.