If the druid (in normal form) takes damage, then uses wild shape, does healing the wild shape carry over to the normal form hit points? Or does healing only affect the current form?
To answer the first question: No. It would not carry over due to how Wild Shape works.
The reason: The only reason damage carries over is because you automatically revert when your HP is reduced to 0 in beast form. This means that damage is dealt after you revert technically.
However, if you revert as a result of dropping to 0 hit points, any excess damage carries over to your normal form.
Therefore the carry over of damage between forms is delayed damage to your caster form until you revert. No effect of healing causes you to revert to receive the extra restoration of hitpoints lost.