Debit cards do work international depending on there brand.
Mine works globally, but I do need to let the bank know. They'll release it for 17 days, after which it gets flagged again.
I haven't ever had a problem ordering overseas. I occasionally buy books from an aviation seller in England. It may be more difficult going the other way; I haven't tried to buy much from the US when outside the country...just usually get what I need locally.