Yes, yes it can. It all depends on the contract you sign. At present, it seems as if most tech shops allow you to moonlight on your own boxes. But I've looked over company policies which were "we own your brainz". HP circa 2006 was one of those, iirc.
No, it literally can't. It can be somewhat similar with contracts that promise a transfer of IP, but you'd get sued for breach of contract, not for copyright infringement.
That doesn't stop companies from putting draconian claims in their contracts and manuals, and it doesn't stop them from trying to prove infringement anyway (no copyright case ever is a 'sure thing'), which is enough to scare most employees into toeing the line. But they can't actually make unrelated work you do on your own time automatically 'work for hire'.
The pivotal words are "within the scope of his or her employment" - these words can get a little fuzzy, but http://www.wisegeek.com/what-is-scope-of-employment.htm is a reasonable (though not authoritative) discussion of the topic.
