Remember that as a freefall observer the spacetime around you looks like Minkowski space (assuming tidal effects are small), and you'd see changes in the magnetic field propagating just as they would in any piece of flat spacetime. The Schwarzschild observer watching from infinity would observe something rather different, but then the Schwarzschild observer would never see you pass through the event horizon anyway.
Incidentally, it doesn't matter where you jump from you will always cross the event horizon at the speed of light. Well, we have to qualify that because in GR this sort of statement is meaningless unless you clarify the frame of reference. Supoose you have a shell observer (e.g. a rocket hovering) at some distance $\delta$ outside the event horizon, and the shell observer measures your speed as you flash past. The shell observer measures your speed to be less than the speed of light, but as $\delta$ tends to zero the measured speed will tend to $c$. We have to use a limit because you can't have a shell observer at the event horizon.
Response to comment:
A shell observer at distance $\delta$ from the horizon will never see anything fall through the horizon, just as the Schwarzschild observer will never see anything fall through the horizon. This is because for those observers the time dilation of the falling object becomes infinite at the horizon. Both observers would see the falling object slow and ultimately freeze at the horizon.
This is why you have to be so careful in defining what you mean. A shell observer can measure the speed of a falling object as it passes, and as you put the shell observer nearer and nearer the event horizon this speed will approach $c$. However once the object has passed the shell observer, that observer will see the object slow and ultimately freeze at the horizon.
I must admit I'm not sure what the shell/Schwarzschild observers would see happening to the falling magnet. I suspect they would see the dipole frozen at the surface.
Your point about hair isn't relevant, because only a static black hole has no hair. By static I mean its properties are time independant, and obviously if you have objects falling in to the black hole it isn't time independant. You would need to isolate the black hole and wait an infinite time for all it's hair to fall off.
It's commonly forgotten that a Schwarzschild black hole is an idealised solution that cannot exist in any universe with a finite lifespan, so the restrictions of Schwarzschild black holes don't necessarily apply in the real world.
It's a very common misconception that black holes suck in matter. Outside the event horizon the gravitational field from a black hole is just like the gravitational field from normal matter with the same mass. The black hole can't suck in matter because matter will orbit it just like matter orbits a normal star.
It's likely there are a lot of black holes in Andromeda's central bulge simply because there are lots of old massive stars in Andromeda's central bulge and this type of star tends to form a black hole as it ages. The black holes orbiting the galaxy core won't fall into it unless there is some way they can lower their angular momentum. This can happen if they pass close to other stars. Interactions between two orbiting bodies can lower the angular momentum of one body and raise the angular momentum of the other. In a galaxy this is known as dynamical friction, and it tends to make heavy objects move inwards and light objects move outwards. Eventually the effect will cause many of the black holes to merge with the central black hole, but the timescale is much longer than the current age of the galaxy.
See Are galactic stars spiraling inwards? for some more info on this effect.
Best Answer
By black hole most of us mean the Schwarzschild metric, but the Schwarzschild metric is time independant i.e. it represents a black hole that has existed for ever and will continue to exist for ever. So it has no age in any useful sense of the word.
The problem with real black holes is that, as discussed at some length following Hawking's recent paper, Scwartzschild observers (i.e. you and I) will never see a true event horizon form. The best we will ever see is an apparent horizon. So if you consider a black hole to exist only if it has a true horizon then we can't assign an age to a black hole because none exist.
I'd probably go along with the pragmatic view expressed in BMS's answer. If you take the black hole at the centre of our galaxy it seems a bit pedantic to point out that it only possesses an apparent horizon, and therefore isn't really a black hole, when its worldline certainly leads to a black hole whether we'll be around to see it or not. Most of us would judge the age of the black hole to be about the age of the Milky Way.
Viewed this way, you're really asking about the age of the black hole's surroundings, whether it's a galaxy like the Milky Way or a supernova remnant as in BMS's example. You'd judge this age as you would for any similar cosmological body.