The Torn-Sky Blast is technically a Mugen Tenshin Ougi, so Ryu should not be able to use it; he's not part of their village. The attack that Ayane used in DOA2 is the same attack she used in the ending for DOA4. That is her own trademark Ninpo attack; this is why it sometimes has a purpleish hue as opposed to looking like white lightning. The only people known who can use it are Hayate and Raidou, and possibly Genra. Hayate was actually taught the technique, and Raidou used his copy skills ability to copy the move after Hayate used it in the battle that crippled Hayate. Genra might have learned it since he was the leader of the Hanjinmon sect of the Mugen Tenshin, as well as Kasumi and Hayate's Uncle. He uses a similar looking attack during his boss battle in DOA3.