Should I re-treat (3rd time) a plantar wart, that has black spots, with Compound W Freeze Off? Child, 10 yrs.

OTC wart treatments. Yes, you can continue to treat the wart, but follow the directions carefully. If the area becomes red and swollen, go see the podiatrist. Those little black dots are the small blood vessels that "feed" the wart. The acid/freeze compound is designed to destroy the small blood vessels which will in-turn make the wart die and fall off. Warts are viruses.
Depends. If you see that it is still there, it may need re-treatment.Plantar warts are quite resistant to treatment and may require many more if you are using this OTC product.