I will call this friction, rolling friction.
It is not called rolling friction. It is static friction. Static friction is the friction force that prevents relative motion between the tire and the road (prevents slipping) where they contact, and which enables the car to accelerate forward.
Rolling friction is due to the inelastic deformation the rubber of the tire experiences when it is in contact with the road. It in involves friction heating. See this article on rolling resistance from Wikipedia: https://en.wikipedia.org/wiki/Rolling_resistance
On the other hand, if the car is stopped on the road and I try to push
it sideways, a friction from the road to the tires of the car will
oppose my force. I will call this friction, perpendicular friction,
because the surface of the tires experiences a friction perdendicular
to its rotation direction.
OK, but it is still called static friction. Static friction is equal to and opposite of the applied force, regardless of the direction of the applied force. So when you attempt to push the car sideways, the static friction force opposes your force until, and if, you are able to push hard enough to exceed the maximum static friction force of $μ_{s}mg$ where $μ_s$ is the coefficient of static friction between the tire and road, $m$ is the mass of the car, an $g$ is the acceleration due to gravity. When that force is reached, relative motion (slipping) between the tire and the road where they contact is impending.
When a car turns, as it is stated in other posts, a friction radially
inwards appears in order to balance the outward movement of the car
caused by inertia.
It is clear that this friction force is directed radially inwards.
Correct. The friction force directed radially inwards is called the centripetal force.
When the front wheels turn, the rolling friction keeps the car moving
forward.
As I said previously, it is static and not rolling friction that keeps the car rolling forward without slipping. More accurately, static friction enables the car to turn without skidding. The cars inertia, if the car is in neutral, keeps it moving. Rolling friction actually results in heating and takes away the kinetic energy of the car causing it to slow down if coasting. Rolling friction increases with under inflated tires. A car will "coast" a shorter distance with under inflated tires because of increased friction heat losses.
But is this rolling friction, and only the rolling friction, while the
front wheels are turned, also the cause of this radially inward
friction?
Once more, it is static friction that provides the radially inward force, not rolling friction.
When the car turns and the front tire moves to one side,can only the
static force in the direction of rotation of the tire provide this
radially inward movement ?
I'm not exactly sure what you mean by the front tire "moves to one side". But in order for the vehicle to not skid in the direction it was traveling prior to turning, the maximum static friction force acting radially inward (centripetal force) during the turn cannot be exceeded by the inertia (centrifugal force) that is attempting to keep the vehicle moving in the forward direction.
Hope this helps.
