Doing some quick math, the transistor will have a base current of 5 milliamps, which a Pi should be able to supply. At a fairly typical beta of 100, the transistor could drive the fan at up to .5 amps, which is plenty for a small fan. A MOSFET transistor is generally better suited for switching high current loads, but for this a BJT (as drawn) should be fine.
Any strong magnet can magnetize other things, depending on the material. Iron can be relatively easily be magnetized, while neodymium magnets require a huge (but obtainable) field.
That looks like a big electromagnet, from a motor, it will probably work, but you have to feed it DC, not AC. (Or else the object will be demagnetized when removed)