It's not problematic to have more than one goal node in A* if you just want to reach any goal node. You simply keep running the search until you have expanded the first goal node.
Provided that your $h(x)$ function is consistent (or just admissible if your graph is a tree) the way of breaking ties does not affect the optimality of the search. As A* always expands all nodes with $f(x) \lt C^*$ where $C^*$ is the true cost of the optimal solution, and never expands nodes with $f(x) \gt C^*$, the number of nodes that gets expanded will end up being the same (or almost the same, as we will see).
Consider this case: We have two nodes $a$ and $b$, who are both on the open list, and we have that $f(a) = f(b)$ and $h(a) \lt h(b)$. We choose to expand $a$ because of the lower $h$-value and discover that a goal node $g$ is a neighbor to $a$. As $h(x)$ is at least admissible the actual distance between $a$ and $g$ can not be shorter than $h(a)$ and therefore $f(g) \geq f(a)$. There are now two cases:
- If $f(g) \gt f(a)$, then we also have that $f(g) \gt f(b)$ and we therefore need to expand $b$ before we can conclude that we have found the fastest way to $g$.
- If $f(g) = f(a)$, then we also have $f(g) = f(b)$, but this only happens if the distance between $a$ and $g$ is $0$ and in that case $h(a)$ must also be $0$. We now have both $b$ and $g$ on the open list and their $f$-value is the same and so we expand $g$ as it is a goal node. In this case we do not need to expand $b$.
Had we expanded $b$ first, the exact same thing would have happened and we would have had to expand $a$ as well unless $h(b)$ was $0$. In other words, taking the lowest $h$-value first has no influence on the number of nodes expanded unless it is the case that $h(x) = 0$, in which case it does make sense to expand this node first. Note however, that only if the actual distance from $x$ to the goal is also $0$ (it could be more that $h(x)$) do we actually save a node from being expanded. So while A* always expands all nodes with $f(x) \lt C^*$ and never expands nodes with $f(x) \gt C^*$, the nodes with $f(x) = C^*$ could be expanded or not expanded depending on your tie-braking and the structure of the graph.