Does Islam support pedophilia or child marriages?

Everyone know that Prophet Muhammad (peace be upon him) married Ayesha (RA) when she was 6 and consummated when she was 9. 1. So, does it mean Islam supports child marriages? If at all muslims consider Prophet Muhammad's (peace be upon him) case as exceptional, then why? 2. Also, a related question, Does Islam support Pedophilia by any means? Answers are expected quoting historical evidences. And also any rulings based on Qur'anic verses is expected along with. *Answers are expected from all schools of thought and sects* ***This question is put up because, many non believers are in a notion of this, and imagine if someone asks you, and you could not answer.*** **EDIT:** OK. Those of you guys who are getting stuck at the age of Ayesha(RA), you can take help from this Age of Ayesha (AS) at marriage? . But don't take it as final plz. **Seems there has always been the controversy regarding the age of Ayisha(RA).**