Electrolytic refining of copper
To your first question: Consider what happens if you put an iron nail or a zinc pellet into a copper(II) solution: the less noble metals will oxidize and reduce the copper ions to copper(0). So even if some of the less noble metal ions are reduced and deposited at the cathode, they would react with the copper ions (that are the most numerous in this scenario).

To your second question: if ions of more noble metals than copper were in the solution, they would be deposited on the cathode. However, by carefully tuning the voltage and current, no more noble metal ions are produced at the anode. As stated by Ivan Neretin in the comments, the cathode will reduce what is available to be reduced: copper ions (which are most numerous and the potential fits).