I don't think so. I have a regular Kindle and a Kindle Fire and the USB cable on the regular Kindle does not work with the Kindle Fire. But I think a USB cable shared between two regular Kindles might work.
YES! Kindle is an ebook reader device from Amazon.
probably
Yes it does.
Yes it does. I have it myself. What the app does is it connects you to amazon kindle bookstore where you could download books just like you would on a kindle.
no they do not work AT ALL with them
Children work rarely in Romania: they help sometimes the family at home.
Yes, the Kindle app can work in airplane mode as long as you have downloaded the books beforehand and have them saved on your device.
A kindle will still work if the battery is low, but it is then recommended to turn the wireless feature off (First option after hitting the 'menu' button). After the low battery warning appears on the screen, the kindle can still render dozens of pages if wireless connectivity is turned off. Connecting the kindle to the computer to use the kindle software is not a problem, as the kindle is charged from the usb connection.
No you can't set up a wallpaper on the kindle fire. it wont work. there is no possible way.
Romania
If it's a standard kindle, you should be able to reset the name by navigating to the 'settings' through the main menu and selecting the option for changing the device name. The kindle must be connected to the internet for this to work so that the online registration of the kindle updates at the same time.