Hi everybody, im really glad i found this site, im not too smart into electronics, so i apologize for dumb questions.
The Only Dumb Question is the one not asked, remember that, if you don't speak up, you'll never know.
Okay, so you say you want to build a magnetic flashlight eh ?
Well, some of your ideas are on the ball, some are not.
The 12v battery may be a bit too powerful, re-read the earlier posts to find out what battery may be best. I'd think 3-6v would do.
If you plan on using a pic pen as your case, I'd say go with something a lot smaller battery wise, probably 2 lithium watch batteries, or maybe 2 hearing aide batteries.
Now the magnetic recharger needs to have 2 poles that stay relatively stable, and get a constant charge, so a spherical magnet may not be the best idea, I'd just say stick with a rod magnet, another thing you must remember, is that those wires will be conducting electricity, nothing too high in volts/amps to hurt, but enough to get hot, not hot enough to melt plastic, but enough to make you drop the flashlight, so I'd make them inside the pen.
So my best idea would be to get the rod magnet, and get a nail about 1mm larger in diameter than the magnet, so it can move back and forth freely.
Tightly wrap the wiring using a thin wire, most likely enamel coated copper to generate more electricity, not necessarily a higher voltage, but the more coils the magnet passes through the longer electricity is generated.
As for the rest, it's all up to you, so you have the final decision.