How the owner can tracked when he widthraw to euro from an exchange site?
If the owner sent bitcoin to an address that is known to be owned by the exchange, then people can see that he sent to the exchange. Only the exchange would know who that was. Since the exchange has identifying information, they will also know who withdrew from the exchange, but others may not know this.
And one last question, if he never widthraw and do only btc payments how he can be tracked?
If the owner of the address posted the address somewhere online, it may be possible to tech who owns the address. It may also be possible to see what services he is sending to by knowing what addresses are used by services.
However, it is fairly hard to track payments and it is not possible to track the ip of the address.