I can't answer definitely about the washers, but I'm pretty sure that they are the old top loaders, and are not HE. Since we have an HE machine at home, I just bring my HE detergent along with me.
I do know that Disers have been routinely using the Purex 3 in 1 sheets at WDW since they first came on the market. They're just so darn convenient for travelling. At least thats what has been reported.