As far as I can tell from reading forum comments, it's not possible to heal the horse yet.
For the balcony woman, the next part is triggered by scenes after making potions for village locals (stay at home and click next to the bed to wait for citizens).
For peeping tom, you can swim at different times, eventually in 'Secondary Quests' it will read 'to be continued in the next update' when you can go no further.
Personally, it makes sense to me that there would be different events depending on which of the girls interacts with a character, though a lot of the time they are interchangeable. One thing which is confusing is that Annie is offered a little job in the tavern but she always refuses to enter.