Is there a minimum age below which a juvenile cannot be prosecuted in JP court for a Class C misdemeanor? This doesn't seem to be addressed by PC 8.07, or any other statute I can find.

You are right that it isn't real clear - but check out generally Chapter 45 in the Code of Criminal Procedure which sets out procedures for handling "children" in Municipal and JP court and look specifically at 45.058(h)which defines "child":
"(h) In this article, "child" means a person who is:
(1) at least 10 years of age and younger than 17 years of age;
and
(2) charged with or convicted of an offense that a justice or
municipal court has jurisdiction of under Article 4.11 or 4.14."