Generally, yeah, ordering from another country works the same way as ordering from your own country. The only exceptions are that shipping will likely be a lot more expensive and that you might have to pay customs on arrival of the package. Hard to estimate how expensive these will be, but I'd say something between 15% and 30% of the price of the goods you ordered can be expected (though cheap goods are also often free of customs, at least from my experience, so if it's just a single average-priced DVD, you might be fine). Of course shipping will also likely take a lot longer, unless you go with the more expensive shipping options, but those are usually dramatically more expensive (for example, it's not unusual to see something like $10 for the cheapest shipping method and $50 for the most expensive one - though in a lot of cases, expensive shipping options include pre-paid customs, which is definitely a plus). Basically, if you go with the cheap shipping options, expect to be waiting for at least two to three weeks.
You should be able to order from Amazon UK with your Amazon US acount, yeah. Amazon should have an international account system. I've used my Amazon Germany account plenty of times to order from Amazon US, so I'm pretty sure other combinations work just as well.
Another important thing to be aware of that applies to your specific situation: Commercial DVDs are actually region-locked. That is, DVDs have a region code on them and can only be played back on devices with the same region code. Unfortunately, the US and the UK have two different region codes for DVDs, so if you are going to order these DVDs, you likely won't be able to play them out-of-the-box. You will need either a region-free DVD player for that or a DVD player with the UK region code. In the US, it's very unlikely that you would randomly have either of those at home, so if you end up ordering the DVDs, you will likely also have to order a region-free DVD player from somewhere. Note that this region-locking also applies to DVD drives in PCs, so don't expect to get around the region-locking simply by playing the DVD back on a PC.
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