In answer to your question about how massless photons can exert physical force, there is some rule-changing going on, but in this case the culprit is not small scales (and hence quantum mechanics) but incredible speeds (and hence relativity).

Remember E = m c^2, Einstein's famous equation that everyone quotes but hardly everyone understands? Among other things, it expresses the fundamental unity of MASS (m) and ENERGY (E). This unity means that as an object's energy increases (that is, as its speed increases), so does its effective mass. The equation for the increase in energy with speed is:

           m0 * c^2
E = -----------------
       sqrt(1 - (v/c)^2)

where v is the speed of the object, c is (as always) the speed of light, and m0 is the "rest mass" of the object: its mass when not moving.

[Side note: if you expand this equation in a power series, you get E = m0*c^2 + (1/2)m0*v^2 + (3/8)m0*v^4/c^2 + ... The first term is called the "rest energy" since it is independent of the speed and depends only on the rest mass, and should look familiar as Einstein's famous equation. The second term should look familiar as the classical expression for kinetic energy. The remaining terms are corrections to the classical kinetic energy, which all involve powers of c in the denominator and are therefore negligibly tiny when the speed v is much smaller than c, as it is in almost all everyday events.]

It is true that photons have zero rest mass, that is, m0 = 0. However, they are never AT rest; by definition they are always moving at the speed of light, v = c. Thus the equation for energy becomes 0/0, an indeterminate value. This gives mathematicians headaches, but in practical terms it means that equation no longer applies; instead we use a different equation for the energy of a photon:

E = h * n

Where n (actually the Greek letter nu) is the frequency of the light (the inverse of the wavelength) and h is a universal constant like the speed of light, called Planck's Constant.

So photons, although massless (or more precisely rest-mass-less), do have energy, which depends on their wavelength. And it turns out in relativity that MOMENTUM, and thus the capacity to exert force, actually depends on the energy of a particle (or equivalently, its mass adjusted for velocity effects) rather than its rest mass. Thus photons have momentum, and when they hit something they can transfer that momentum.

This result doesn't depend on being at small scales. When you shine a flashlight on something, each photon that hits that object actually does exert a miniscule force on it. But because macroscopic objects have such immense masses (and hence inertias) compared to that force, we don't observe any resulting change in motion. It's only at small scales that the masses of particles are small enough for their motion to be noticeably affected by being hit with a photon.

I hope this explanation is clear! Let me know if you want any more clarification. As always, great job and keep up the good work.