I am scared of enabling the Sync because my smartphone is on Wifi and I think this Sync will cost me money is it true or ?

If your phone is on wifi there should be no additional costs. Though your internet service provider would be more knowledgeable about your specific internet connection costs. Depending on your usage the First sync can be about 10mb of data. Keeping the two devices in sync uses a very minimal amount of data maybe 0.01-0.001mb per sync event. In addition the Firefox Sync service does not have any charges or fees.