To my knowledge, baby zombies can't break doors at all. I just tested having one aggro a villager through a wooden door, and the baby zombie did not break the door. If you'd like to test it yourself, go into creative and test it using ' /summon Zombie ~ ~ ~ {IsBaby:1} ' (The ~'s denote your current x,y, and z coordinates).
To cure a zombie villager, a player must splash it with a splash potion of weakness and then feed it a golden apple. The permanent discount is capped at 5 cures, while the temporary discount is capped at 8 cures. In Java Edition, players can also gain negative reputation by hitting or killing villagers, and positive reputation by trading or .