http://www.pathname.com/fhs/
If you only want one user to use it, you can install it in your home directory. If you install it in/usr/local it would ordinarily be accessible to all. However, you can mess with the permissions and restrict it.
You wouldn't exactly 'install it in bin'. The binary would go in bin and other files would go in their appropriate places.
/bin is supposed to be for binaries needed by the core system that may also be needed by regular users at regular times. /usr/bin is where more general applications go. /usr/local/bin is reserved for the sysadmin (you) to install whatever he wants and not have it messed with in an upgrade. Also, these various filesystems can be mounted from separate partitions and shared with or reserved from certain other machines on the network.
As far as non-standard locations, it depends on the program. Some programs will operate fine in isolation. But if you install a library in a goofy place, it's a headache to tell every other program that needs it where it is.
Windows gets away with the 'all parts of an app in a directory' through a couple of means - everything is a desktop or menu shortcut and *not* everything is in one place, contrary to what people think. A lot of configuration is here, some libs are there, bits and pieces are recorded solely in the registry. And few people know where everything is. But besides that, it's just a different philosophy.
However, it's not much easier to move stuff around in Linux. It's made easier by symlinks but why would you really want to do that anyway?
But reading that link above should answer a lot of things better than I can.