You are thinking in terms of atoms and molecules and you are mainly talking of solid state matter .
Solid state is another quantum mechanical phase, it has lattice structure with much smaller energies than atomic and molecular transition structures. Lattices have vibrational levels which are mainly responsible for the black body radiation solids emit, infrared is also photons.
A rule of thumb with radiation impinging on solids is that if the wavelength is smaller than the lattice dimensions the photons can penetrate easily the lattice, interacting only with direct scatters hence the higher penetration of X rays and gamma rays. Here is an article that discusses the penetration of radiation, X rays and higher.
For glass and optical frequencies there is a good answer here in this site., essentially the structure of the transparent materials is such that the photons pass through without loosing energy in the visible.
For infrared where the wavelengths are large in comparison with lattices or distances between molecules in liquids, the photon can give up its energy in collective excitations at the surface gradually heating up the material.
For ultraviolet, glass, depending on the type, has some absorptive bands, the photon energy transferred at the surface to collective modes or breaking molecular bonds and transformed to heat ( infrared) further in.
So your
Once you reach a critical frequency, however, the photons will begin to be absorbed because they have enough energy to excite the electrons (which is why glass is opaque in ultra-violet).
has small probability to happen until x-ray energies are reached which are the energies of bound electrons, and the link above gives the dependence in a simplified manner.
Well, it's better not to argue about words ... but I would say, that it makes more sense not to consider the photoelectric effect as ionisation. (There is no ion produced anyway, is there? :))
There is nothing special about charges in metals (and there is also nothing special about the slow free electron produced), and nothing "bad", whereas ionising radiation is associated with bad things like cancer etc.
The electron was not tightly bound to an atom anyway, there are plenty of those free electrons in the metal, and you can move them and thansfer them to other pieces of metal with simple electrical fields. The effect has much more in common with heating the metal than with ionisation. You do something to a big reservoire of electrons, not to a single atom.
My conclusion: one can definitely argue which radiation is potentially ionising (see comments to the question), but clearly this very process is not an ionization.
Best Answer
Yes. In the normal scale view of an observer, it looks just like an ionization (in fact, it is). And since they're knocking out the electrons of atoms, you can visualize this effect as ionizing radiation. Well, wave-particle duality can be taken into account for explaining why energetic gamma rays and X-rays are grouped under Ionizing radiation category which consists of alpha, beta, etc. particles...
Yes. There is quite a large connection. I think you've got yourself confused while writing the question. Photoelectric effect is the effect caused by EM radiation. Gamma rays, X-Rays (being an EM wave, or particles if you want) have photons of high-energy and hence, they knock-off electrons.
Like I've already said, both are same. Ionization by EM radiation = Photoelectric effect.