When I add the potassium thiocyanate to the iron(II) solution, I see a faint red colour. Why is this?

Unless the iron(II) solution is freshly prepared, it is likely that some of the Fe²⁺ ions will have been oxidised to Fe³⁺. These Fe³⁺ ions will react with the thiocyanate ion to give the red colour change. 

When I add the potassium iodide solution to the iron(II) solution, I still see a faint blue-black colour. Why is this?

As with the previous answer, an iron(II) solution will often contain some Fe³⁺ ions due to oxidation. Therefore, some of the iodide ions will be reduced to form iodine.

Why can't the Fe³⁺ ions reduce the silver ions to form Fe⁴⁺ and silver?

Looking at the successive ionisation energies for irom can help us.

• The 2nd ionisation is 1562 kJ mol^-1.
• The 3rd ionisation energy is 2957 kJ mol^-1.
• The 4th ionisation energy is 5287 kJ mol^-1.

We can see that the 4th ionisation energy is much larger than either the 2nd or 3rd ionisation energy. Consequently, it is rare to observe the formation of Fe⁴⁺.