Random comments:
"Absolute Maximum Ratings" is not useful for planning suitability of the component, except when something goes horribly wrong.
While the part indicates 3V to 5V signal voltage, the ratings clearly indicate 5V is intended, 3V will work for function, but will have a large impact on the current it will carry (large reduction in current before overheat).
Capacity in most of these cases is not strictly "amps" but RDS
(ON), which limits by calculation how much the device can handle without overheating. That limit may be below the current limiter in your application and design.
Inductive loads (solenoids, incandescent bulbs, etc) are especially hard on devices like this, and require careful planning and calculations for a good choice.
Use your basic MOSFET calculations for power, resistance and watts versus degrees/watt (thermal resistance) spec for your design.
Don't guess, or believe the sales pitch, or take perfect laboratory condition limits as guidelines. Calculate. The results will likely be far different than your expectation.
Hope that helps.