If someone didn't light Channukah lights on the first night, does he/she then say the third blessing (Sh'hecheyunu) on the next night?
Yes. Recite birkas shehechiyanu on the second night after the regular two b'rachos. The same goes for any subsequent night if it is the first time you are lighting this year. (Shulchan Aruch Orach Chayim 676:1)