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?
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.
It's for you to judge if the following is relevant.
"Another example of a drastic change in surface properties by one-atom-thick layers can be a silicon monocrystal surface. When the surface of a silicon plate is etched in hydrofluoric acid (in order to dissolve the thin native oxide layer), the atoms of silicon on the surface are terminated with hydrogen atoms. This makes such a plate hydrophobic – drops of water do not wet the surface. But when we wait for some time or put the plate into deionized water for a few tens of minutes, the SiH groups on the surface slowly change to SiOH, and the water starts to wet it completely. This effect of only one atom change on the surface is visible by the naked eye (Lehmann 2002)."(http://books.google.com/books?id=LcenAAAAQBAJ&pg=PA43&dq=%22one+atom+thick%22+silicon+-%22graphene%22&hl=en&sa=X&ei=neOWUo6iNMLPrQGP1IHgAw&ved=0CDoQ6AEwAg#v=onepage&q&f=false )
The above is not about "one-atom-thick sheet", but about "one-atom-thick layer", furthermore, it is not clear if the layer is visible or wetting/non-wetting water, but this is more relevant to "tangibility".
This was just asked on another forum last week, a student from Penn State made a sheet of graphine to see for himself. He reported that he could not feel the sheet, but he could see it.