No Errata
Q: Does Skitter-scurry allow me to push the upgraded fighter twice when I make a Charge action?
A: Yes. You can push the fighter once after the Move action, and once after the Attack action (as long as your opponent does not play a reaction first). Note that the Move action must still end with your fighter in range to make an Attack action (before the push) or the Charge action cannot be made. Similarly, if the push takes your fighter out of range to make the Attack action, that Attack action cannot be resolved.
Q: Does Skitter-scurry allow me to push the upgraded fighter after each separate Attack action in an Attack action that targets multiple fighters (e.g. Whirling Halberd), assuming my opponent does not play a reaction first?
A: Yes. However, the only fighters you can target are those who were adjacent at the start of the action, and your fighter must be in range of each of those fighters to make an Attack action against them. If the fighter is pushed in such a way that they are not able to make an Attack action against any of their remaining targets, no further Attack actions are resolved.