Assuming a reasonable pressure (no trains with flanged wheels trying to drive down the highway) then the damage comes from axle load and not pressure for standard road building materials.
Yes but the strength of materials is usually measured by elastic modulus which has the same dimensions as pressure. Hence, although a bike will elastically deform a small area of the surface with the pressure it applies, it will deform it more than a car with lower pressure tyres. However I doubt this is where the damage comes from but rather from the motion of the vehicle. The dynamic load of a car travelling at speed will be many, many times greater than a cyclist who is less massive and slower moving. Similarly for lorry it will be many times larger still than a car. We would need an engineer to confirm but I expect that this is where the damage comes from since the dynamic load can be many times larger than the static one.