Manganese or Magnesium.

Non-metal (lustrous) = Iodine (I)
Metal (non-lustrous) = Sodium (Na)

Metal, because metal oxides are basic in nature.

Zinc being more reactive than iron displaces iron from iron (II) sulphate solution. Thus, the green colour of the solution fades and iron metal gets deposited.
Zn(s) + FeSO₄ (aq)  \(\rightarrow\) ZnSO₄ (aq)  + Fe (s)
Zinc      (Green)              (Colourless)   Iron (Deposited)
 

Sodium metal being reactive highly reacts so vigorously with oxygen that it catches fire if kept in open air. Therefore, to protect it from accidental fires, sodium is kept immersed in kerosene oil.

Since the metal X react with cold water, it must be high in the reactivity series i.e., sodium or potassium.
X is alkali metal, Na or K.
Since the metal Y reacts with hot water, it must be middle in the reactivity series i.e., magnesium or calcium.
Y is alkaline earth metal, Mg or Ca.
Since the metal X reacts with steam only, it must be low in the reactivity series i.e., iron Z is Fe.
Increasing reactivity series : Na > Mg > Fe.

(i) 3Fe(s) + 4H₂O(g) \(\rightarrow\) Fe₃O₄(s) + 4H₂(g)
     Iron      Steam           Iron oxide   Hydrogen
(ii) (a) Ca(s) + 2H₂O(l) \(\rightarrow\) Ca(OH)₂ (aq)         + H₂(g)
     Calcium   Water             Calcium hydroxide   Hydrogen
(b) 2K(s) + 2H₂O (l) \(\rightarrow\) 2KOH (aq)             +    H₂(g)
 Potassium   Water      Potassium hydroxide     Hydrogen

(i) 2Cu + O₂ \(\longrightarrow \) 2CuO
(ii) 4A1 + 3O₂ \(\longrightarrow \) 2A1₂O₃
(iii) A1₂O₃ + 2NaOH\(\longrightarrow \)2NaA1O₂ + H₂O

(i) Because it forms a protective oxide layer around itself preventing complete reaction and also does not affect the food at all.
(ii) Calcium floats over water because the bubbles of hydrogen gas formed sticks on the surface of the metal.

(i) X - Carbon, Y - Diamond, Z - Graphite
(ii) Non-metal
(iii) Tin.

Three properties of sodium are:
(i) Sodium is so soft that it can be cut with a knife.
(ii) It has low density.
(iii) It has low melting point.