Not necessarily. If you only use Windows, it makes no sense to have different file file systems, as FAT32 is rather inefficient and Windows 2000/XP/Vista default to NTFS anyway. If you dual-boot with Linux, you should use different file systems, as Linux doesn't handle NTFS very well, Windows can't read Linux partitions (like ext3 or ReiserFS) at all without additional software, and FAT32 is unsuitable for both. If you use Linux by itself, you can use multiple file systems without any issue, although sticking to one may be easier for performance or maintenance reasons (ReiserFS is faster; ext2/3 has more widespread support in various recovery tools).
No, for example one partition could be formatted NTFS, another FAT, another Apple HFS+, another XFS, etc. Your OS may not support access to all these types of filesystems (at least without extra drivers added), but the harddisks can support being partitioned that way.
Most hard drives have only one partition. Each partition is formatted according to one file system. So most hard drives have only one file system. However, many hard drives have two or more partitions. One common approach is to "dual boot" a computer, with Linux on one partition in the ext4 file system format, and Windows on another partition in the NTFS file system.
In the normal sense of a "file"system, swap is not formatted as a file system. It is formatted similar to memory or RAM.
The most likely reason is that it is not formatted, or the file system on it has become corrupted.
An extended partition is simply that, a partition. It may be formatted with a file system or it may not. Of course, in the latter case, it will be of no use.
The formatting using its own file system is logical drive.
NTFS
FAT File system
A quick format simply erases the file control structures on the partition such as the Master File Table (MFT) on NTFS formatted partitions or the File Allocation Table (FAT) on FAT(32) formatted partitions. A full format also checks the drive for bad sectors and, upon encountering any, adds them to the drives internal list of bad sectors so they will be completely ignored and unused by the file system. When formatting a new disk for the first time or a disk with unknown history it is better to perform a full format. If you are just reinstalling your operating system on a known good drive then a quick format will suffice.
Under Windows, a floppy drive is always formatted using the FAT 12 file system.
Volume
Yes, you can. If the external hard drive is formatted using the FAT32 or NTFS file system then you can read it in any windows computer. If you have it formatted as one of the Linux file systems (EXT2, EXT3, JFS, etc.) then just pop in an Ubuntu Live CD into the computer that you want to retrieve the data with and copy it off.
It could mean that the external HD is formatted with a file system that your OS can not access. If thisa is the case, either reformat the HD with an appropriate file system or install and boot to another Operating System (and maybe be unable to acess the files you already have on your computer)