Can a magnetic field of an object be stronger than its gravity? Can a planet, star or otherwise have a magnetic field that is stronger or have more range than its gravity?
It depends on what object it's acting on.  There are many objects, including stars, that have magnetic fields where Lorentz forces on charged particles like electrons and protons are stronger than the gravitational force on them. 

Also remember that the strength of the Lorentz force depends on the speed of the particle moving through it, so a fast enough moving electron even here on Earth will receive a larger magnetic force than a force of gravity. This is how the Earth's magnetic field is able to contain charged particles in the Van Allen belts that its gravity could not contain.