Yes you can use the device while it is charging. As Far as the first part of the question it all depends on the size of the battery you get. This one 6000mAh so it has enough power to fully charge the kindle and then some. The battery on the kindle fire is rated at 4400mAh so the 6000mAh portable battery would more than double the amount of time you have, plus it is portable so you can charge while you are on the go. They also have some batteries that are 10000mAh, if you need that much more capacity. Only thing I would say is that it does take a while to charge the portable charger, but otherwise super handy, and if your kindle fire uses the mirco usb to charge, like almost all android phones do, then you won't have to worry about carrying and extra cable for charging! Hope this helps.
Not sure about the Kindle Fire. I don't have one. But I know it will charge 3 iPhones that are very low on juice and you can use them while you are charging. It doesn't take long to charge either. Hope this helps. Have a blessed day!