Is acceleration necessary to define force?

There is acceleration. The car decelerates, accelerating backwards, when it hits the wall, and either the wall breaks and accelerates or the earth accelerates by some tiny bit as the equal and opposite reaction.

The situation is complicated somewhat by the fact that the car is being crushed and the wall is being damaged, consuming some of the energy of the impact. There is however a perfectly clear notion of acceleration here, it’s just a tad bit more subtle than in many typical physics class examples.

The link between the forces acting on a body of mass $m$ and its acceleration, $vec a$ is this:

$$sum vec F= m vec a$$ in which $sum vec F$ is the vector sum of all the forces acting on the body, sometimes called the resultant force.

As the car hits the wall much the largest force acting on the car is that from the wall. This force dominates $sum vec F$ so the car has a very large acceleration in the direction of the force (that is 'outwards" from the wall). Call it a deceleration if you like.

I assume that your concern is that the wall experiences a huge force from the car but doesn't accelerate noticeably (assuming that the wall isn't demolished by the impact). But it is the resultant force that gives acceleration, and the wall is, we assume on firm foundations. These foundations exert a force on the wall that is very nearly equal and opposite to that from the car. If the foundations are unable to exert this force, then the wall will accelerate, in other words it will topple over.

It is, in my opinion, an oversimplification to define a force in general as that which gives a body an acceleration. It is resultant force that does this.

As @TheEnvironmentalist already pointed out, the car will decelerate when it is brought to a stop after impacting the wall.

Now, if you know the stopping distance $d$ of the car (the distance its center of mass moves between initial contact with the wall and when it stops) and its mass $m$ and its velocity $v$ just prior to impact, you can calculate the average force $F_{ave}$ the wall exerts stopping the car using the work energy theorem which states that the net work done on an object equals its change in kinetic energy ($mv^{2}/2$).

$$W_{net}=F_{ave}d=frac{mv^2}{2}$$

Hope this helps.

There is acceleration (deceleration). When the car hits the wall it either stops or goes back. Anyway the velocity changes so does momentum. As rate of change of momentum is defined as force there is force acting on the wall as well as car(third law of motion).

Hope this helps.

A force can exist without causing any acceleration. In this case the there are multiple forces acting some of which cancel out. Therefore not all forces will cause acceleration

So technically speaking, forces are independent of acceleration