consistent heuristic - does it always exist?
The zero heuristic is trivially admissible, as you've noted. It's also trivially consistent as long as all step-costs are non-negative: if $h(x)=0$ for all&nbsp;$x$ and $c(x,y)\geq 0$ for all $x$ and&nbsp;$y$, then
$$
h(x)\leq c(x,y) + h(y)
$$
for all $x$, $y$.