Why is the cyclopropenium ion aromatic?
It does meet Huckel's rule.  When you have $m$ carbon atoms in a conjugated ring with a positive charge of $q$, there are $m-q$ pi electrons.  Here $m=3, q=1$ therefore the number of pi electrons is $m-q=2=4×0+2$.

A Huckel model calculation indicates that cyclopropenyl cation has roughly as much stabilization as benzene, but it's distributed over three instead of six carbon atoms.  Thus aromaticity is especially powerful in a cyclopropenyl cation ring.   This explains how a positive (formal) charge can be stabilized on as few as three carbon atoms and the ring holds together despite steric strain.