In Minecraft, there is no way to heal zombies. Because of its undead nature, even splash potions with healing can cause damage to the zombie.
According to legend, zombies will eat your flesh. There is not much you can feed a zombie. They don't seem to be eating any food. They do drop potatoes and carrots so it is possible that they like the earthy vegetables.
Unfortunately, you cannot cure a zombified piglin. There are two possible outcomes for a zombified porklin. It would be difficult to determine if the cured zombified porklin would become either a piglin, or a pig. There is no way to cure a zombified porklin.
A splash potion of weakness and one golden apple can cure zombie villagers. However, you can cure zombie villagers without having to make the potion yourself. If you can find a witch, they may be able to give you a splash potion. Trap a zombie villager, and drag a witch between the two of you. You can get the witch to throw a weakness splash potion and feed the zombie villager with the golden apple.