Definitely yes. Gold is surprisingly transparent for a metal. Famously, gold plating is used on astronaut helmet visors, at 200 nm thickness - i.e. ~1200 atoms thick.
Not transparent at all on visible light wavelengths. Light transmission in metals obeys the skin effect, which means that AC fields (such as the fields in light) do not like to penetrate deep into the material, and the skin depth for visible light wavelengths in most metals is expressed in individual nanometers.
It is also used as a coating for window panes, as it‘s great at reflecting infrared radiation (reducing heat loss). My father‘s house has such windows.
Stealth aircraft also use gold-plated canopies to a) contain emissions from the cockpit to the cockpit b) reflect incoming radiation of a well-defined surface instead of whatever mess is inside the cockpit.
If I am reading that right, the beaker is filled with lots of sheets and clumps of sheets not just a single one. So, it’s not clear what if anything a single sheet would look like.
How about this: two objects are touching when the interaction forces between the objects are of similar magnitude to the interatomic forces within the objects. Very generally speaking, this will happen when the distance between the objects is about the same as the distance between atoms within the objects.
To be somewhat pedantic: "touching" is a word. The extent to which it is or is not an "exact science" depends on what is meant by "touching", and by "exact science". The definition I gave of "touching" could be made arbitrarily more precise by specifying more precisely the interaction forces under consideration, and the level of precision to which one should compare their magnitudes. What you mean by "exact science" is something I cannot guess at with any useful level of precision. Whether or not any of this has any bearing on the original topic of discussion is another matter.
That was sort of my point. If we use a definition of "touching" that is relevant to the atomic scale, whatever that definition is, we can reasonably talk about what "touching" means at an atomic scale. If we use a colloquial definition of "touching" which is meaningful for macroscopic objects but not at the atomic scale, it doesn't make sense to talk about "touching" at the atomic scale.