A Kite is a quadrilateral with two distinct pairs of adjacent sides which are equal. A Kite has two pairs of equal sides in which each pair must be distinct disjoint and must be adjacent to each other, sharing a common vertex. This means, the pairs cannot have a side in common. Only one pair of angle which is the angle between the unequal sides is equal to its opposite angle. The diagonal are perpendicular to each other and longer diagonal bisects the shorter one.
Kite Picture
In the figure above, ABCD is a kite with AB and AD as one pair and BC, DC as another pair of sides which are equal and share common vertices A and C respectively. AC and BD are the diagonals of the kite. The diagonal AC bisects the diagonal BD. And, $\angle$ABC = $\angle$ADC.
    
In real life, kites can be seen being flown in the sky as a game with a different shaped tails.
The length of the diagonals of a kite can be found by using Pythagoras theorem.
Kite Diagram                                    
Let the diagonals AC = $d_1$ and BD = $d_2$. Then $d_2$ bisects $d_1$ and so AO = CO = $\frac{d_1}{2}$.
 
Using Pythagoras Theorem, OB = $\sqrt{AB^2 - AO^2}$ = $\sqrt{AB^2 - (\frac{d_1}{2})^2)}$.

OD = $\sqrt{(AD^2 - AO^2)}$ = $\sqrt{AD^2 - (\frac{d_1}{2})^2}$.

From the figure, the diagonal $d_2$ = BD = OB + OD = $\sqrt{AB^2 - (\frac{d_1}{2})^2 )}$ + $\sqrt{AD^2 - (\frac{d_1}{2})^2}$.
 
Area of a Kite: The area of a kite is half the product of its diagonals. The formula is given by:                     
Area of Kite = $\frac{d_1 d_2}{2}$  where $d_1$ and $d_2$ are the lengths of the diagonals.
Perimeter of a Kite:
The Perimeter of any polygon is the total distance around the outside of a 2-dimensional shape.

A kite has two pairs of equal sides. In the figure above say AB = AD = a and BC = DC = b then the formula can be stated as:
Perimeter of a Kite = 2a + 2b where a and b are the lengths of each side in each pair of equal sides.

Yes. Every Rhombus is a kite, as Rhombus satisfies all the properties of kite. A kite with opposite sides parallel becomes a rhombus. Thus every Rhombus is a Kite but not every Kite is a Rhombus.