"How "sharp" is a 1 atom thick hammock...if you walked into it what would happen?" and other microscopic questions

Taken from this comment chain: http://www.reddit.com/r/todayilearned/comments/1cadub/til_a_1m_hammock_made_from_a_singleatom_thick/c9encli

1. How "sharp" is a 1 atom thick hammock...if you walked into it what would happen? Would you just go through it unharmed? (from Fearless_fx)

2. What if you had an even thicker graphene rope (like 20 atoms) and tried to choke someone with it? Like would the rope just pass right through him and decapitate him at a cellular level and leave him unharmed? or would it be the cleanest decapitation ever? (from The_Dee)

And I have a few questions of my own. How "thick" would a graphene sheet have to be to have a noticable amount of wind resistance? And would a blade of this material be a useful cutting instrument?