As Unix isn't any particular operating system, there is no distinct name for the kernel. Different versions of Unix may have vastly different kernel structures. The Linux kernel is called, well, the Linux kernel. The Vista kernel is a continuation of the "NT kernel" designed for Windows NT 3.1.
Linux is the name of a Unix-like operating system kernel. Ubuntu is an operating system that uses the Linux kernel.
To create a free Unix-like kernel that other people could study and use.
The Linux kernel is named for its creator, Linus Torvalds. The practice of appending an X was for Unix and Unix-like systems.
Linux is an operating system, like Windows, that runs on the Linux Kernel, which is based off of UNIX.
The "basic concept" of Linux is a free and open-source Unix-like kernel.
In truth, there is no "linux system" per se'. There is the kernel, developed by Linus Torvalds, properly called "Linux" but a kernel alone is not a system. Most operating systems that run on the linux kernel are unix-like derivations, but not all.
Linux is the full name of the kernel. It was created as a combination of the phrase "Linus' Unix", after the original author, Linus Torvalds.
No, but Linux is based on Unix since Linux is a Unix clone.
The kernel is the lowest layer of abstraction in any OS, including Linux. It takes care of the core components of a system, and manages the hardware.