I'm making some kind of pi-pad. But the screen needs a 12v input.
Does anyone of you know a small battery which has an output of 12v?
The second thing would be on how to recharge these?
I've seriously looked everywhere but couldn't find a solution.
If you have looked everywhere but didn't find a solution then why do you think a solution exists? .
Does 97 x 43 x 52mm fit your definition of small? Search for MM22 at maplin.co.uk. Alternatively you can put 10 NiMh cells in series. Or use a lower voltage battery and a step up converter.