How far out does the sun's gravitational pull extend?

Yes, the Sun has a gravitational influence on everything in our solar system. But, the Sun's gravitational influence is not a good marker for determining the edge of our solar system because there is no definitive point or drop off to which you can say this is the end of the Sun's gravitational influence. The same can be said about the Sun's light.

Many people prefer to use the heliosphere as the solar systems edge marker which is the dominance of the Sun's solar wind over interstellar space.

The Sun contributes to spacetime across the Universe.

Beyond the Oort cloud, the Sun does not bind objects to an orbit.

http://en.wikipedia.org/wiki/Oort_cloud

"Does it encompass everything in our known solar system?"

The orbits define the solar system. If they orbit the Sun, they are part of the solar system.

"Is that how we define what is our known solar system?"

That and that we know about them. There is a possible 4x Jupiter's mass, named Tyche, that we have yet to "know" exists. We should have disproof, or a viable observation "by the end of 2013":

http://en.wikipedia.org/wiki/Tyche_%28hypothetical...

http://en.wikipedia.org/wiki/Tyche_%28hypothetical...

http://arxiv.org/abs/1102.0212

It's technically infinite, but it's reasonable influence goes far past the end of our solar system. It's also not very clear where the end of our solar system ends.

The sun's gravitational pull is generally (*) the strongest gravity out to about 1.2 light years. Beyond that, the gravity of other stars and the rest of the galaxy takes over. After 12 light years, it is almost impossible to detect the gravity of the sun.

(*) I say "generally", but there are a few small bits of rock and gas that have their own gravity, that is stronger than the sun if you are very close to them. We call these bits of rock, "planets".

It extends out until it reaches another objects gravitational force of equal or greater value .

When you drop something does it fall to the Sun or the Earth ?

Even though we call it a gravitatiomal force it is now understood to be curved space warped by mass .

If you could view space with gravitational lines it would look like concenctric sphears close to dense massive objects with straighteng less curved lines were gravity equals out.

The suns gravity extends an infinite distance, however its strength decreases to the square of the distance, so twice as far away it will be four times weaker, ten times as far away, a hundred times weaker and so on.