First, to answer the first two questions.
Static friction prevents relative motion between surfaces. It is non dissipative, meaning it does not generate heat.
Kinetic friction occurs when there is relative motion between surfaces, e.g., slipping, sliding, skidding, etc. Kinetic friction does generate heat due to the rubbing between surfaces. Rub your hands together rigorously and you will feel them warm up. That's due to kinetic friction.
Rolling friction if more properly called rolling resistance. Rolling resistance is the result of inelastic deformation of the material of a rolling object, such as the rubber of a tire, when it contacts the road. The material compresses when it contacts the road and decompresses when it leaves the road during each revolution. The squeezing and un squeezing of the material generates internal friction and heat. Think about a metal spring. Rapidly compress and uncompress the spring. You may feel the metal get hot. This is due to the inelastic behavior of the spring.
For more details on rolling resistance, see this article from Wikipedia: https://en.wikipedia.org/wiki/Rolling_resistance.
More area of contact will increase adhesion then why is friction not
dependent on area of contact and moreover friction is a contact force?
First consider kinetic friction. The equation for the kinetic friction force is
$$F_{k}=\mu_{k}N$$
Where $\mu_{k}$ is the coefficient of kinetic friction and $N$ is the force normal (perpendicular) to the surfaces.
The normal force $N$ divided by the area of contact $A$ is the pressure between the surfaces. Although increasing the area results in a greater source of friction forces, when you increase the surface area for the same normal force $N$, you decrease the pressure between the surfaces. The increase the friction generating area is offset by the reduction in pressure. For this reason the friction forces are dependent only on the friction coefficient and the force holding them together.
Next consider rolling resistance. From the Wikipedia article
$$F_{r}=C_{rr}N$$
Where $C_{rr}$ is the coefficient of rolling resistance. Unlike the coefficient of kinetic friction which depends primarily on the types of surfaces involved, the coefficient of rolling resistance also depends on dimensional factors. For tires, they include the dimensions of the sidewalls and the contact area of the tire.
So rolling resistance does depend on area of contact, but it is incorporated into the rolling resistance coefficient.
Hope this helps.