Witch Dedication feat (page 222) explicitly states (paraphrased):
a) you don't get other effects from the patron
b) your familiar gets the normal number of familiar ability points vs. what a witch would normally get
c) explicitly covers how many cantrips received from this dedication
However, it doesn't make specific mention of whether a familiar received would have either the Learning Spells nor the Undying ability covered in the Witch's dedicated familiar section (page 181).
I have seen discussions online giving opinions ruling both for and against granting the above. I feel that since the Witch Dedication feat specifically mentions changes to the patron and both the number of cantrips and familiar abilities, but makes no mention of Learning Spells nor Undying that is covered by the Witch's Familiar section, that it is intended they have both. Unsure if this was answered more definitively elsewhere.
The above alone would not have prompted this post. Unless I am misreading something, one or both of these feats:
Basic Witchcraft (page 222)
Basic Lesson (page 186)
are broken. I can take these feats:
Witch Dedication (giving access to a few Cantrips) at level 2
Basic Witchcraft -> Basic Lesson at level 4
All of the Basic Lessons covered on page 185 give the familiar a 1st level spell, but the Witch has no way to cast the spell with only the above feats. I assume this is not intended.
It could be fixed by making Basic Witch Spellcasting a requirement of Basic Witchcraft, but that then only leaves one Witch Dedication feat at 4th.
Maybe a 4th level feat giving the Witch access to the hex spell and ability normally given by a Patron (but not the 1st level spell)? Or would that be too powerful?