The anime is set 40 years or so after the original cartoon, and the girls are descended from their original incarnations. They all moved to Japan for some reason.Would at least explain why the PPGZ aren't sisters. The original PPG all married different men. In Japan, for some reason... maybe they developed a strange collective fondness of Japanese guys in their teens or something. The PPGZ didn't directly inherit their ancestors' powers, but the incident with the Chemical Z activated them, explaining where the theme-colours and Super Hero names came from all of the sudden... from their genes, of course.
There are Bunny and Bullet in PPGZ, just not as the PPGZ and indirectly.Since this was not stated by the creators of PPGZ, this should be a WMG. Bunny's PPGZ counterpart is Miko, Himeko's big sister, while Bullet's PPGZ counterpart is Kuriko, Momoko's little sister. They sure have a lot in common, with a few twitches though.
Miko Shirogane is one of Bunny's fantasies.Bunny wanted to be treated with love, so she became Miko, who's all perfect and well-respected. She was later driven to hatred when she saw the PPGZ because they remind her of the PPG who don't give her as much attention as she had now.
Ken Utonium grew up and got involved in the creation of Brain Burst.Apparently, Chemical Z accesses the subjects' deepest traumas and desires to give them superpowers. Ken somehow figured a way to emulate Chemical Z's effect into the virtual world. Thus, Brain Burst works the same way, but only in the virtual world.