Onsider a galvanic cell in which al3 is reduced to elemental aluminum, and magnesium metal is oxidized to mg2 . write the balanced half-cell reactions that take place at the cathode and at the anode.

Two Half Cell reactions are as follow,

                                    3e⁻  +    Al⁺³    →  Al            (Reduction Reaction)

                                    Mg   →   Mg⁺²  +  2e⁻           (Oxidation Reaction)

In order to balance the number of electrons, multiply reduction reaction by 2 and oxidation reaction by 3.
So,
                                    6e⁻  +    2 Al⁺³    →  2 Al           

                                    3 Mg   →   3 Mg⁺²  +  6e⁻           (e⁻ cancelled)
                               

                               2 Al⁺³ + 3 Mg  →  2 Al  +  3 Mg⁺²

Result:
            At Anode Magnesium metal is Oxidized and At Cathode Aluminium Ions are reduced.

They are like other investigations? say there was a murder u have to do blood test and finger prints which run through a lab. 

Use a magnet to separate iron, evaporate water, i'm not sure how to separate the other two i'm sorry but good luck