No. The correct question would be "Can any motherboard go into any computer CASE." And there are several different sizes of case standards.
Like Gazaway said generally speaking no although I think ATX cases can accommodate most smaller motherboards.
Ya, I'm pretty sure the safest way to go would to get a BTX case, I'm pretty sure they can fit BTX and ATX form factors.
Not necessarily. The mounting holes would need to be there for an ATX board. Also, since the BTX push is basically dead (Intel pretty much said it's done trying to pimp it), unless you absolutely need a BTX case, I really wouldn't waste my time looking for one. BTX cases can acommodate smaller BTX sizes, like pico BTX. ATX cases can accomodate ATX and micro ATX/mATX/uATX. Actually, they should work fine with DTX as well, since DTX is even smaller than mATX and designed to sit alongside it.