Are you a visitor from South Korea or a Japanese resident from South Korea? If you are just a visitor then SoftBank will not sell you a 3G iPad. They will only sell them to residents of Japan. But your nationality doesn't matter, as long as you are a resident.

There is no identification or any requirements at all for the wi-fi only model.

All iPads are unlocked. And I don't think pre-ordering is needed anymore. I noticed at Yodobashi Camera in Akihabara that they now have all the models in stock.

There is no problem with a foreigner getting a 32 GB 3G model as long as you are a resident of Japan and have sufficient proof of that. There is a list of requirements showing you have residency that are posted in the forums. In my case just showed my Japanese driver's license. There are other variations allowed such as your alien registration card plus a credit card, etc.