Your answer in #1 is wrong. Remember LEORA-GEROA (Lose electron oxidation reducing agent, Gain electron reduction oxidizing agent)
16H+1 + 2MnO4-1 + 10Cl-1 ---> 2Mn+2 + 5Cl2 + 8H2O
Mn is not a reducing agent. A reducing agent is supposed to undergo oxidation. Mn undergoes REDUCTION, Its oxidation number goes from +7 to +2. Meaning it gains electrons since its number decreases.
Cl is the reducing agent since it undergoes oxidation. Its oxidation number goes from -1 to 0, meaning it loses electrons and tends to lean more to the 'positive side'. (Cl2 is a free element, so its oxidation number is 0)