IMO it doesn't matter how magnetization occurs.
Yes you can make a pickup with any magnet and a piece of wire. But I guess you want to make a telecaster pickup? Do your homework, plenty info available. Once you figure out what exact kind of pickup you are trying to copy, just get the correct parts. Magnet strength is important, and I don’t know how you’d adjust it if you are not in a factory setup? Wire gauge and insulation are important, for tone, but mostly they determine the maximum length of wire (or number of turns) that you can wind around a specific bobin. Also the most difficult part for a beginner might be counting the turns. How are you going to do it?