No clue, sorry - I have a Nook (I was purchasing back before Kindle offered sharing and library borrowing).
If the trick with the iPhone works, you can always re-link that to the account afterward - there will be times when you don’t want to lug the ereader with you and it’s nice to have a few books on the phone (I have some on my Droid and my iPod Touch).
On my Kindle for Mac, I have my books grouped into collections (basically, by genre). I found some on line instructions to import those collections to other devices, but I can’t seem to find the indicated menus. Is this functionality no longer supported?
Doesn’t exist, I’m afraid. Many other people want a shopping cart for Kindle; perhaps Amazon will listen.
Change your Kindle’s name to something that comes alphabetically earlier than “I” to put it in front of your iPhone.
Right now my Fire HD is “Hominem Unius Libri Misereo”, roughly translated as “I pity the man of a single book.” But I’m not very good at Latin, so I’m probably wrong.