When you initially apply power to a solenoid (it's an inductor, remember) there is a large current which is required to charge the magnetic field and actuate the solenoid. Once the solenoid is actuated, not as large a magnetic field is required to hold the solenoid actuated. From a magnetic point of view, you've got a piece of metal some distance away from an electromagnet. You need a certain amount of current to generate the field to move that piece of metal. Once the metal piece has moved closer to the electromagnet, you don't need as much current to hold the metal piece.
No, you can't use a MOSFET to drive an AC solenoid, it would only work for DC. You'll need to use a solid-state relay or something else.