In a strong field, how long would it take for domains to align? How fast is the rate of "switch" for the domains to align with an exterior field? Possibly in milliseconds? 
I assume it won't take much time since domains are very small, and they only turn from a certain degree to another.
I know this would depend on a lot of factors, but if powerful large magnet can attract a ferromagnet with a force of nearly 4,000, brining it closer to it would take 0.005 seconds, then surely the magnetization was a lot faster than that. Since magnetization occurs before attraction. 
 A: http://news.sciencemag.org/math/2012/02/hot-idea-faster-hard-drive : "Each bit in a magnetic recording medium is in fact a nanometer-sized patch or "domain" that can be magnetized in either of two directions—say, up and down—to encode a 0 or a 1. That information is read out by the read head, a tiny electromagnet that passes over the rotating disk and measures each domain's orientation. The same head also writes the information to the disk by applying a magnetic field that flips a bit's orientation. But the traditional electromagnetic read head struggles to keep up. For a while now, the time needed to write one bit has been stuck at about 1 nanosecond, limiting the rate of data transfer."
A: I agree with the above quoted evaluations for the magnetization switching, but a precisse calculation concerns solving the Landau–Lifshitz–Gilbert equation (http://en.m.wikipedia.org/wiki/Landau%E2%80%93Lifshitz%E2%80%93Gilbert_equation) 
and particullarly knowing the value of the damping factor alfa. The phenomenological character of this parameter is a great difficulty and only experimental works and numerical simulations can elucidate this issue. Fortunately, there are now several works that point values in the region of microwaves.
