I just started, I'm on lesson 3 and using Anki.
I notice that when I finish it says "next time 20 new cards"
Is that 20 frames from the book? I see that some characters are just primatives and have no frame number, just an asterisk.
So do the 20 new kanji include those as the 20? Or is it 20 new frames plus the primatives?

The primitives with an asterisk don't appear on their own in the deck. So yes, 20 new cards is 20 new frames is 20 new kanji.