my wife had her period for 6 days then stopped for 3 days then it happened again for 5 days , the question is, is it period or not? And what about fasting and praying?

Yes, this blood is considered from her menses provided it came out within 15 days from the beginning of her period. This is because the maximum period for menses is 15 days. Therefore, your wife must refrain from fasting and prayers until she is completely purified from blood and subsequent dark discharge or after 15 days from the beginning of menses, whichever comes first.