Q:

Is an atom-thick sheet of a material visible and tangible?

If one could make a sheet of a material (thickness of an atom), Aluminum for example, would it be visible to naked eyes? What about tangibility? would it be tactile by human finger skin?

A:

It is extremely hard to say what would happen because the only way to reliably test those regimes is to do it experimentally. Single-atom thin layers have only been realized, so far, in graphene, which is a single layer of hexagonal carbon crystal, and which is strong enough to exist by itself without any support. The Wikipedia section on its optical properties will inform you that

Graphene's unique optical properties produce an unexpectedly high opacity for an atomic monolayer in vacuum, absorbing $πα ≈\ $2.3% of white light, where $α$ is the fine-structure constant. This is "a consequence of the unusual low-energy electronic structure of monolayer graphene that features electron and hole conical bands meeting each other at the Dirac point... [which] is qualitatively different from more common quadratic massive bands".

Thus, graphene is surprisingly opaque - for a monolayer material. It absorbs more light than you'd expect, and if you look carefully you can probably see it with the naked eye, but it's still pretty transparent.
I'm unsure what its response to the human touch is, though it is reported to have a huge tensile strength.

