Gravity dictates the orbits of the planets around the sun. By measuring those orbits, you can calculate the planet's gravity.
No, that's not true at all. The mass, and therefore the gravitational pull, of a planet (unless it's a giant planet) is so infinitesimally small compared to that of its primary star that it basically goes to zero in the equation. The only significant factors defining a planet's orbit are the mass of its primary star and its distance from that star.
A planet's surface gravity is calculated from its own mass and radius. Its orbital parameters have nothing to do with that computation.
Here on earth, we have a normal gravitational force.
No, here on Earth we have an Earth-sized gravitational force. We think of that as "normal" because it's what we're used to, but there's nothing intrinsically more "normal" about Earth's gravity than that of any other body.