1st: Of course. You really don't need an operating system to record multiple loops.
You may need some kind of OS support if you want to load or save files or data, control input or output, but this can also be done directly with the BIOS functions: read the key from the keyboard, write to any screen or LED or serial interface . Only if you want to run several programs or deal with interrupts from the outside, conflicting resources or such, then you desperately need an OS.
2nd: The kernel is compiled into machine code, which is executed at boot time. No C at kernel startup. C helps to write only the kernel or any program that should run if in the kernel or "bare metal".
rurban
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