Could a "sunbrella" parked at L1 block enough solar energy to counter global warming?
There are several journal articles on this topic, for example Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.  

Being truly at the L1 point is unsuitable because the radiation pressure of the photons acting on the shade (like solar sail) would disrupt the equilibrium, so the equilibrium point is shifted toward the sun from the L1 point and depends on the degree to which the shade reflects versus absorbs.

The shade should be made of black material to minimize the effect of radiation pressure on the equilibrium point, thereby permitting it to be as close as possible to the L1 point, and closer to the Earth, where it can more effectively shade.

The size required is roughly a 1,500 kilometer diameter structure.  

All parts of the Earth would be shaded to some degree. From Earth, the sun would appear as it does during a transit of Venus or Mercury, but the position on the sun's disc would vary more with ones location on Earth since the shade would be much closer to Earth than Venus is.