I know that systemd and SysVinit have their own projects and are developed independent of the Linux kernel.
But what about the classic init system? where its source code located? is it part of the Linux kernel? or somewhere else?
SysVinit is the classic init system. Reference A history of modern init systems (1992-2015)
Where GNU/Linux is concerned, the most common chronology given is that first there was sysvinit.
It is not part of the Linux kernel but would be part of any "base operating system", since the OS has to run something once the Kernel is loaded.
The source code is located at http://svn.savannah.gnu.org/viewvc/sysvinit/