Sue of Maine gave me some great advice. I've also gone into the rec.gardens archives. Conclusion - wave petunias have to be deadheaded and are far from the absolutely carefree plants that the sellers promote, at least in a hanging basket.
Since comments in the rec.gardens archives often seem to contradict each other, here goes with my questions.
Sue tells me to "pinch off the seed pods". Does that mean pinching off the whole little stem that the flower was on? I've a zillion of them.
The hanging basket is now about four or five feet across because of straggly growth with flowers just at the ends. I'll cut it back after I hear from anyone.
As Sue said ("doG - I hate petunias") she would forgive me in August if I dumped the whole basket on the compost heap. However, it's a gift, and a challenge to someone who doesn't know what the h*** she's doing. The "gifter" will be here this weekend and I'd like to defend myself!