The symetrical airfoil at zero angle will produce zero lift.

Here's a great little site with FoilSim on it. You can play with thickness, camber and angle of attack and see the effects on lift and drag and a few other things. It's a great educational tool for this sort of stuff.

http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html

Use the "Shape-Angle" tool to set the parameters of the airfoil. You can also see the total lift for a given size wing that you can change or the lift coefficient. Plug in some model numbers and you'll get a much better idea of what our stuff does.

Kites, planes, hands..... they all work the same. Parachutes are different unless they are the paraglider types or other airfoiled types. Then they are a wing and react the same. The basic domed emergency chutes of days gone by are just drag producers. No flight stuff. To have lift there needs to be an airflow across the object.