Zombie Heroes, fight like heroes or zombies

[Zinthos]

Rulebook Page 19: Zombie Heroes work just like normal Zombies with the following exceptions: (there are 3, none are relevant)
[1: move faster, 2: hero style wounds counts, 3: none of the former heroes special powers ]

So Zombie Heroes fight exactly the same way Zombies do, for the same reasons and with the same dice, which have the same meaning. So they are no better than regular Zombies in a fight, except maybe having a slightly better unlife expectancy due to the higher wound count.

For the other part of you question, YES, a regular Hero still needs a double to cause a Zombie Hero to take One Wound, just like he would need to cause a regular Zombie a Wound. The difference being one wound typically see a regular zombie off the board, while a Zombie Hero will usually have 2-4 wound slots.
Fending off a Zombie Hero causes no more harm to it than Fending off a regular Zombie does (ie none). Otherwise, it would be clearly listed in the Exceptions list in the rules.

Brother-in-Law's are EVIL, I suggest you feed him to the next Zombie you meet.