When you trade on Morpher you do so on our Sidechain. The sidechain is blockchain, like Ethereum, but one that we supervise. Like any other blockchain it takes fees to place orders. However, transactions on the sidechain are free, because we give you virtual ETH (you can see this on the funds page), and top it up for you every night, and that's what is used to pay these trading fees.
The only fees you actually incur is when transferring your tokens from the sidechain to the mainchain (real Ethereum blockchain).