Plain RSA with $3$ primes, find all integers $x$ so that $x$ is equal to $y$ when $y= e_K(x) = x^{b} \bmod n$
If I understand correctly, you are looking for the integers $x$ such that, for all $b$, $x^b \equiv x \pmod n$.

You almost have it!  You've correctly identified $x = 0$ and $x = 1$ as solutions.  If you had a solution $x$, what can you say about $x_i := x \bmod p_i$ for each $p_i$—how are $x_i$ and ${x_i}^b$ related modulo $p_i$?  Can you use the solutions $x = 0$ or $x = 1$ modulo $n$ as inspirations to find solutions modulo $p_i$ and recombine them into solutions modulo $n$?