The kernel is the main core of an operating system which manages certain tasks in including memory allocation, paging, process management. It interacts with interrupts from hardware and also from software through syscalls.
A piece of software which translates source code made on one machine into machine code for another architecture. The most common platform for kernel development is i686 and is 32 bit.
When a computer is turned on an initial piece of software is triggered and ran which is called the bios or uefi. This executes a bootloader which then runs an operating system. Common bootloaders include grub and they load in the OS into memory.
A program can be recognised as a kernel by a bootloader by initialising some special variables in a header. From here it knows exactly how to load the kernel.
A stack is a reigon of memory in which variables are stored. A good analogy for a stack is a pile of books. One can add more and more books onto this pile, however to retrieve any book you must also remove any book on top of it. This is where the idea of pushing and popping registers comes from. In x86, the stack grows downwards thus if it starts at 0xAB5, the next location will be 0xAB6.
A linker combines object files into a single executable file. Linking is when we collect various bits of code from multiple sources into a single file which can then be executed. Linking is how a simple hello world program in C can use libraries like stdio to utilise the printf function as it combines bits of code together. We need a linker to link our assembly code to our high level language as I atleast don't want to write my kernel in pure assembly.
Static linking happens at compile time and combines code with a library whilst dynamic linking happens at run time.