How many are there? Also what is the size of those domains?
Finally, when domains align with exterior magnetic fields do they move or are they all fixed? I assume they are all fixed because the atoms in a materials that have there dipole moments are fixed?
Hard questions. The number of them probably depends, for starters, on the size of your material. Knowing the size of them could be easier to do, but only as an expected value (statistical in nature) or if you want a distribution of sizes.
This distribution would depend on the crystal structure, the magnetic structure, the strength of the magnetic interactions (which depends on the structures mentioned before), crystal impurities (grains, ions, level of polycristalinity) and on the temperature among other variables.
Regarding the application of an external magnetic field. It would depend on the system and on how related are the domains with impurities of the crystal structure. In principle they realign (again in a statistical sense) and eventually the domains reorganize and coalesce.
Keep in mind that one of the reasons of the formation of domains or walls is an entropic effect where for the system is entropically favorable to have a misalignment even when it costs energy to do so.
Hope I clarified a bit those questions.
