Can app store purchase be shared with a Mac running older version of Mac OS X?
An install on Mac OS is generally just copying the relevant files into place. Usually, you'll be able to copy an app's bundle over from one machine to the other. The only thing is that the App Store will have some sort of DRM, so just copying it may not work. I suspect that the answer is no, because you'll need to sign in to the App Store, but I haven't tried it. (On the other hand, I've installed Lion on a Leopard machine via a disk without Sow Leopard.) Additionally, Apps that are downloaded from the Mac App store will carry minimum system requirements that might prevent them  from running altogether, even if you theoretically circumvented the DRM from the App Store.