I also managed to install fine on FF first time, even with adblock and noscript.
The reason that you are taken to the US site for your books is that the UK site does not sell eBooks, even if you have an international Kindle. Those lucky people that have one buy the device and every book or newspaper from the US website. I can see the credit card companies licking their lips as they think of all the currency exchange fees they will collect.
As for the free books, I managed to get one on my PC. Finding them is tricky - for some odd reason Amazon keep showing the ones you need to pay for...
I found a list of them by using the listmania feature.
An interesting point to note is that even if the item is free, you still need to enter credit card details to get the delivery. I used a fake card number (which is designed for testing card processing systems) and got the book. Although it did tell me the card had failed, which suggests they do run the card, even if they do not take any money.
On the point of not being able to get the choice of all the books in the UK, I suggest you just either register a US amazon account and/or change the option in the software for what country you are in. I don't think you can do this with a Kindle as they know which phone network you are connecting on.
The software is not bad, but does not appear to open any files. The only books it supports are the ones you download from Amazon. It also has the notes and annotations option, but as read only. So if you find an error while you check a note you added on the kindle, you can't correct it.