Hi guys! Maybe you wont mind if a monkey butts in? (monkey butts)

Chemist is right on the money when he cites current sizes and difficulty in manufacturing. (Read "difficulty" as "Even throwing millions of dollars at the worlds most intelligent and trained students and professionals isn't working that quickly.")

There are many physical problems with trying to create a crystalline structure that is 1 atom thick.

Once created, you have to deal with the fact that the exact same number of atoms NOT restricted to a plane has a lower energy. This means that even once you've isolated or grown graphene, it must be held in place to prevent it from curling, crinkling, wadding, etc. There are many 3D crystalline arrangements for the carbon atoms to form, so the graphene must be held flat everywhere... you can't just isolate certain nodes, you have to hold the whole sheet.

So even the notion of a "large" sheet of graphene holding a cat is a bit off the scale of practical. The closest you could get would be a carbon composite material, because what would be holding the cat is the worlds thinnest carbon-fiber sheet. Which is still quite cool.

Whether or not it would be transparent would depend mostly on the adhesive/substrate.

If you can touch a smooth lump of coal, then you can touch graphene. You'd destroy the surface crystal structure if you touched it with enough pressure to register on your nerves, so "feeling graphene" is a bit tricky to answer... some of the coal you crushed into your fingerprint might actually have a graphene surface... but on the whole, you're feeling coal dust.