Linux – Difference between /usr/include/sys and /usr/include/linux

What? no /bin/ is not a symlink to /usr/bin on any FHS compliant system. Note that there are still popular Unices and Linuxes that ignore this - for example, /bin and /sbin are symlinked to /usr/bin on Arch Linux (the reasoning being that you don't need /bin for rescue/single-user-mode, since you'd just boot a live CD).

/bin

contains commands that may be used by both the system administrator and by users, but which are required when no other filesystems are mounted (e.g. in single user mode). It may also contain commands which are used indirectly by scripts

/usr/bin/

This is the primary directory of executable commands on the system.

essentially, /bin contains executables which are required by the system for emergency repairs, booting, and single user mode. /usr/bin contains any binaries that aren't required.

I will note, that they can be on separate disks/partitions, /bin must be on the same disk as /. /usr/bin can be on another disk - although note that this configuration has been kind of broken for a while (this is why e.g. systemd warns about this configuration on boot).

For full correctness, some unices may ignore FHS, as I believe it is only a Linux Standard, I'm not aware that it has yet been included in SUS, Posix or any other UNIX standard, though it should be IMHO. It is a part of the LSB standard though.

Linux distributions use the FHS: http://www.pathname.com/fhs/pub/fhs-2.3.html

You can also try man hier.

I'll try to sum up answers your questions off the top of my head, but I strongly suggest that you read through the FHS:

• /bin is for non-superuser system binaries
• /sbin is for superuser (root) system binaries
• /usr/bin & /usr/sbin are for non-critical shared non-superuser or superuser binaries, respectively
• /mnt is for temporarily mounting a partition
• /media is for mounting many removable media at once
• /dev contains your system device files; it's a long story :)
• The /usr folder, and its subfolders, can be shared with other systems, so that they will have access to the same programs/files installed in one place. Since /usr is typically on a separate filesystem, it doesn't contain binaries that are necessary to bring the system online.
• /root is separate because it may be necessary to bring the system online without mounting other directories which may be on separate partitions/hard drives/servers
• Yes, /etc stands for "et cetera". Configuration files for the local system are stored there.
• /opt is a place where you can install programs that you download/compile. That way you can keep them separate from the rest of the system, with all of the files in one place.
• /proc contains information about the kernel and running processes
• /var contains variable size files like logs, mail, webpages, etc.

To access a system, you generally don't need /var, /opt, /usr, /home; some of potentially largest directories on a system.

One of my favorites, which some people don't use, is /srv. It's for data that is being hosted via services like http/ftp/samba. I've see /var used for this a lot, which isn't really its purpose.