The chance is random, but high enough that you wouldn't be spending weeks trying to get them. Just normally meleeing in combat for a while is good enough to get you at least the first 4-5 skills. After that it starts getting a little rare though.
I'm also starting to find it a little hard to keep my party up to date as I can't remove Reimu from the party. She's level 16 currently while everyone else is 11-15, and after acquiring a new party member, I have no space for her right now.
Edit: Well, I only remember 3 hooks in the first strata, and I got Momiji, Sunny Milk, Luna Child, and Star Sapphire for my troubles, as well as the aforementioned recipe.
By the way, do the broken recipe numbers get fixed in 1.03, along with the missing last character of a lot of sentences? And if I used 1.02x to patch my client but it's only up to 1.01, do I have to do 1.02 and 1.03 separately?
Just read the logs and tried the patch. Patch works, and all that was fixed were some minor Shikigami issues.