You have asked some very interesting questions!
1) Gravity does indeed affect light. All light in the presence of a gravitational source either "bends" or shifts its frequency, but unless the gravitational field is extremely strong it's difficult or impossible to detect with the naked eye. Using precise instruments, we can measure the light from a star and determine this effect, which gives us information about the star's gravitational field.
2) Stars, including our sun, are extremely massive but not massive enough to trap light in its gravitational field. That doesn't mean they do not bend light. Some stars actually bend light so much that, were they not millions and billions of lightyears away, we would definitely notice something funky going on. Neutron stars are the densest stars that we are aware of, and if you were a reasonable distance away from one you would be able to see more than half of the star at any time!
That's hopefully a better visual explanation of why you would be able to see more than half of a neutron star. From a "head on" perspective, a neutron star would look like this:
3) There are objects in the universe, however, which have a strong enough gravitational field that no light can escape from a certain region around its center! These objects are known as Black Holes.
4) Light does exert force on other objects, too! That is to say, when you shine a flashlight or a laser on a wall, the light pushes on the wall! Don't get too worried, though. The force is usually very small--powerful lasers exert a force around ~10^-9 Newtons (about the weight of a grain of sand).
I hope this answers some of your questions! You're doing some great thinking.
(published on 02/13/2011)