The battery is built-in and it lasts long for a single charge. 

I have not looked for a specific travel case, but unless you are being really rough with it I would say a padded envelope or a generic small case would do it. It's pretty sturdy. I take it to to the office sometimes and just put it in one of the pockets of my laptop case. Also, for extra protection against scratches I never removed the clear plastic film that comes over the screen. Except for the red ""pull here"" tab, you can't tell it's there. 

Question for the manufacturer. Thin film solar panels are made by other manufacturers. This is the kind of solar panel the average person could afford. Check out "Allpower 100-watt portable, folding solar panel" for backpacking with power bank. 

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I don't know the exact size but it even fits 12-13 year old kids.