What happens to preempted interrupt handler?

As far as I know a ISR can be pre-empted by another interrupt, and continue running after that . I see no reason why a process could be put on the stack and a ISR not.

I'll try to answer 1 of your questions. Answer to 1) ISR can't sleep because they run in the context of the currently running process. If they sleep, the currently running process will be moved to sleep state.

That is undesirable.

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