The weight of the propellant helps hold the rocket on the pad during the test fire, reducing how much force the hold-downs need to exert to keep the rocket on the pad, and stressing the rocket's structure in the same way it will be stressed at launch.
Test fires with a near-empty rocket would put considerably more force on the pad's hold-downs and the corresponding parts of the rocket's structure.
Blue also had a fuelled 2nd stage on top of the booster for the static fire, which is not out of the ordinary.
SpaceX has a "cap" that is held down with cables that it uses when it needs to test-fire a first stage by itself at its McGregor test site; static fires at launch sites are usually done with the 2nd stage on top.
Right. The forces these things produce are massive. I only know the specifics for the Space Shuttle, but when it is at full liftoff thrust (liquid and solid boosters) there's just no way to keep it leashed to Earth. It's going up whether you want to or not.
It is also more realistic to do it fully loaded - very different forces are acting on a rocket based on how much propellant is loaded.