I've bought some books from Amazon for my kindle. Two questions: One, can I (legally) pass the books on to my Mother? Two, if I can pass them on, what's the best way to do it?
You can install a Kindle App on a tablet or PC, and read any of your Kindle books on that as well as on your Kindle. The app would need to be registered to the same Kindle account, which means your mum could buy books that get charged to you. Depends on how much you trust her
Get a hold of Calibre software and store all your books on that, then you can copy them to any Kindle you like.
In Amazon, get the books sent to your own personal e-mail rather than that of the Kindle.”
The key word there is 'legally'. Yes, you can use Calibre to strip off the protection and pass books on. I have done it many times (though I can't get it to handle the new AWZ3 files) but it's not legal.