To summarize--Yes you need that magnet wire, and the Lamination is an alloy of steel and ferrite. That is used over standard steel because this alloy doesnt retain as much magnetism once the magnet is shut off. (think of the trick of dragging a nail across a magnet to magnetize the nail. this Ferrite & steel alloy doesnt retain the magentism.) But for a home project, any steel alloy with a relatively high content of iron will suffice. As for a power supply, All the door lock magnets I've played with never needed any resistors; I was able to hook them up to standard alkalai batteries (9v, and 1.5v), and any DC step-down transformer from 3V to 12v (I never had a 24V step-down transformer laying around to try 24v.) Most of them will run on as little as .5a at 12v. And yes you just need to calculate turns, where the larger the wire, the less turns, where the 27awg I believe is a couple hundred turns or so for a decent magnet. and the steel plate the magnet adheres to that actually lockst the door is usually around 1" (25mm) thick, at least as long as the magnet, and mounted so it the magnet makes full contact to the steel plate.
And the RFID reader is nice touch if I may say so, and easily integrated into this circuit, although I am unfamiliar with the exact wiring of the magnet with an unlocking mechanism, so someone with a greater knowledge than I should probably be able to tell you how to wire your reader into it.
I hope all of this was helpful to you. and good luck with it.