For torque, but very often for inertia. Reflected load inertia falls with the square of the reduction ratio, so even a modest gearhead can bring a badly mismatched axis into a tunable range. Many axes that respond sluggishly or oscillate do so because the load inertia overwhelms the rotor, and adding reduction fixes that far more effectively than selecting a larger motor.

It depends on the accuracy required at the load and on whether the axis reverses under control. Backlash appears as lost motion on every direction change, so an axis that reverses frequently and must position accurately needs a low figure, quoted in arcminutes. An axis that runs mostly in one direction, or where a following error of that size is acceptable, does not, and precision grades cost substantially more.

It is how much the gearhead twists under applied torque, and it determines how the axis behaves dynamically. A compliant gearhead introduces a resonance between motor and load that limits how aggressively the loop can be tuned, so an axis may be stable but slow. On demanding axes, stiffness is as important as backlash and is published alongside it.

Yes, in both directions. It reduces reflected load inertia by the square of the ratio, which is the main benefit, but the gearhead has its own inertia which adds to the motor's rotor inertia. On high-ratio units that addition can be significant relative to the motor. Both effects belong in the matching calculation rather than only the reduction.

Not without checking. The input bore and clamping arrangement must suit the motor shaft, and the pilot diameter and flange must match the motor face. Manufacturers supply adapter kits specified for particular motor frames, and fitting a gearhead to a motor it was not intended for risks poor concentricity, shaft damage and premature bearing wear even where it physically bolts together.

A servo gearmotor is matched to a servo motor with feedback and a servo drive, and is specified on backlash, stiffness and inertia for positioning duty. A planetary gearmotor is a general industrial drive specified on torque, ratio, service factor and mounting for continuous running. The gearing may be similar; the selection criteria and the price are not.

Most precision servo gearheads are sealed with a lifetime grease fill and need no routine attention, which is part of their appeal on machine axes that are difficult to access. Check the manufacturer's position rather than assuming, particularly for larger units and high duty cycles. Watch for any increase in backlash over time, since that indicates wear and directly degrades positioning accuracy.