No. The Planeteers never knew each other before being summoned by Gaia.
In the very first episode, you meet each of the Planeteers on their respective continents. There are numerous references to their backgrounds throughout the series, and it is never established that they went to the same school as children.
As for the similarities, the producers may have done it on purpose, however its more the case they were both going for a diverse group of people.
- Groups of 5 are big enough to allow wide diversity, but not so large as its difficult to differentiate.
- Africans, Native Americans and Asian are both genetically predisposed to black hair. Asian hair is especially straight as both illustrations show.
- Left with an option for a brunette and a blonde Caucasian, they would have wanted the blonde female character as blondeness is an attractive trait in women.
Any other similarities are coincidental as Magic School Bus and Captain Planet were produced by different companies.