1. NTFS allows smaller cluster sizes and a larger number of clusters, file names longer than the "8.3" format (max 8 characters in the name plus 3 in the extension), and more files in the root directory. FAT was designed for DOS and was limited to 256 files in the root directory, filenames like MYFILE1.DAT, and the cluster sizes and maximum number of clusters was fixed.
2. The Unix file system differs in many ways from that of Windows. Unix allows "named pipes", which are FIFO (first in first out) file structures whose contents can be "consumed" (read and then they disappear) from one end and fed into the other. Unix also allows the permissions of read/write/execute by global/group/user. Windows.... well it handles those BASICALLY the same way but there's also a little-known ability to set programmer-defined file attributes AND "programs allowed to execute a file of this type", which is how some viruses spread, by making non-executable files executable by a priveleged program. A good example is you give out a free game for people to download, and the game is capable of "playing" corrupt, infested powerpoint shows that people seem to send to all their friends. That gets past most anti-virus software's ability to block malicious executables... all because of a weirdness in the file system. The Unix file system also uses the "/" rather than a "\" to separate directory names in a fully qualified file path (when represented in the old DOS style notation, e.g., c:\directory1\subdirectory'.) Finally, the Unix file system uses an "inode table" to maintain a list of files in memory, starting with what was read at boot up, plus anything that was changed since then. Windows USED TO maintain the file system on the hard disk and always write to the hard disk, but starting with Windows NT, and for performance reasons, Windows allowed NTFS to use a system similar to Unix, where the list of files was maintained in memory.
3. The Linux / Unix top level directory is "/".
4. Linux supports both the Unix file system.and FAT. Are you sure the question wasn't what OS's does it support? It runs on most Windows boxes, Sun workstations, and quite a few others.
5. The oldest Linux file system? I don't know. It might be FAT or it might be something related to Unix.
I don't know what your professor / teacher is looking for, probably an answer out of a book. But I have worked in tech for the last 20 years, and this is how I learned it in the field. I have personally built Linux boxes and worked with the very earliest versions of both Linux and Windows.
Good luck on your homework. And you might want to check my answers. Just because I remember stuff doesn't mean it's correct.