[1] Contact forces are very common and are responsible for most visible interactions between macroscopic collections of matter.
Pushing a car or kicking a ball are some of the everyday examples where contact forces are at work.
[1] The atoms in the two surfaces cannot penetrate one another without a large investment of energy because there is no low energy state for which the electron wavefunctions from the two surfaces overlap; thus no microscopic force is needed to prevent this penetration.
On the more macroscopic level, such surfaces can be treated as a single object, and two bodies do not penetrate each other due to the stability of matter, which is again a consequence of Pauli exclusion principle, but also of the fundamental forces of nature: Cracks in the bodies do not widen due to electromagnetic forces that create the chemical bonds between the atoms; the atoms themselves do not disintegrate because of the electromagnetic forces between the electrons and the nuclei; and the nuclei do not disintegrate due to the nuclear forces.
Additionally, strain is created inside matter, and this strain is due to a combination of electromagnetic interactions (as electrons are attracted to nuclei and repelled from each other) and of Pauli exclusion principle, the latter working similarly to the case of normal force.