For those who want to access the new stuff as soon as possible, here is a quick run down of what happened to my playthrough
For both new areas:
In the lake, keep searching the area until the text appear saying that a new location has been added on your map, 1 of these locations will included the new spirit Haru
For new scenes:
These will occur during events which come by naturally as days pass by, so just keep passing time but make sure your relationship with the spirits as high as possible
For Moki:
Same with the new scenes, the moki will appear in front of your tent after you have done all of the previous events (atleast in my case), however completing the quest will make it so that you cannot interact with Ori (No spoilers but if you played Will of the Wisps then, :,D )
Edit: the moki scene will be unlocked by calling it cute atleast once and then waiting for in game days after The event