So long as we are still in the EU, Portugal won't get customs charges. The beauty of the custom union that our silly govt want to take us out of is that there are no custom charges between EU countries. So Alkevin won't have any issues that way, at least not till after Brexit happens.
Amazon themselves will ship to you I am pretty sure. The second party sellers may not all. I have this issue with Amazon Japan. The main site will ship to me just fine, but sometimes I have to dig through the individual sellers to find one that will send overseas.
In terms of the shipping cost, it will calculate the actual shipping cost when you go to buy an item, or it should. It should give you the actual shipping cost right before you confirm your order; it won't show it on the individual item pages otherwise. It will happen when you select your address, at which point it ought to note your location and adjust the cost accordingly. Though Amazon have so many EU hubs it is possible that there may be a local hub that will ship the item to you for the same cost as within the UK. That has been known to happen though I am not clear how that system works. I just know that I've had it happen sometimes when buying from the US site.
It might also ask you if you want to pay in Euros or in £. I am not sure about within the EU whether that happens or not.