I like the question because an answer to it will give a better understanding, from first principles, of the underlying algorithms.
So question 1 has two parts:
1a) How does the CryptoNight PoW algorithm work at all?
That's specified here: https://cryptonote.org/cns/cns008.txt
1b) How does it really work, on a low level, looking at elementary instructions?
I'm not familiar enough with the basics of how AES, Keccak and the different hash functions used (blake, groestl, skein) work on a detailed level, but that seems to be the only things that you have to look up.
As for question 2), of course you as a human can perform all the elementary instructions that your computer does when running cryptonight PoW, provided your remaining life span is long enough.
You could e.g. attach a debugger while mining monero, look at the elementary machine instructions that are performed, and repeat them by hand. Obviously a hand held calculator will help to do additions, multiplications etc. faster.