Hi Paul!
Sorry for being so basic with my provided information 
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I connected every 4th of them so basically the LEDs 1,5,9 are one cluster", 2,6,10, etc...
Those should be fading in the same way. -
The only specification I found out are just the voltage which is 1,8V and the max. current is 20mA.
Is this sufficient information? -
Please see answer one
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I would like to have a switch which just turns them off and on, I don't want to change anything by using switches, potentiometers and such...
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I'd like to use a few 1,2V batteries or one 9V block. Maybe I could use akkupacks with those voltages and have them reloaded on a power supply.
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I have, yes!
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Ah, good to know that! Thanks a lot!
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I will try to get a photo of it but since I haven't got any chance to get back home this weekend it's very unlikely I cannot provide it
Hope that explanation of me is sufficient to get an imagination how the LEDs are wired up...