how do people come up with these algorithms???

I completed the kata myself but this solution is greek to me. Guess I have a lot to learn

from a golfing perspective idk why you wouldn't just do n * n for squares, saves a whole 2 characters.

n < 0 && !(n % 2) ? -fn(Math.abs(n))[0] : fn(Math.abs(n))[0]
can be simplified to
n < 0 && !(n % 2) ? -fn(-n)[0] : fn(Math.abs(n))[0]

I would love for someone to walk through this

I fixed this solution here: https://www.codewars.com/kata/reviews/52a78825cdfc2cfc87000008/groups/620b7948793105000108b662

True, nice catch! Basically this happens because this solution does not calculate well the (-3 - 2), it returns -1 instead of -5. It would be nice to add this test to the solution validation.

This solution returns incorrect result for expression:
(2 - 2.5) - (-3 - 2) * (-5)
Returns -5.5, but should be -25.5

What lvl of algs is needed to get this?)

We have to. You can't mix Number and BigInt, so if your base is BigInt, your exponent has to be also. ( It's not so exponents can be ridiculously big. :P )

Right shift (>>)

what does >> do?

.

Why people raise the same issue over and over and over? Maybe because the author didn't fix the issue on time.