I'll have a crack:
1.)In case of dual generator failure. Starting APU and you should connect the GEN 2 first to charge the battery through the TR3. Why? Don´t understand because GEN 2 powers the mainbus and the battery charger is then supplied? Where´s my fault?
What else does TR3 do?
2.) How long can the speedbrake be deployed. I mean with which flap setting? up to flaps 15?
No limit but best not more than F5 due to tailplane buffet - don't want it falling off, do we?
3.)Where in the MEL can I find wether i have to have the athr engaged during the CAT III or not?
Not in MEL - in your AWOPS limitations section - A/T mandatory IF AVALABLE.
4.) Imagine ATHR is okay during CATIII approach and it does not retard. Can i retard the thrust levers on my own? So disconnect the autothrottle and pull them back?
Yes, (or just close them) just do not press TOGA
5.) Is a cat III II landing in contaminated runway allowed? Which penalty must be applied?
LDA check plus what are your AWOPS crosswind limits in your OM?
6.) When the ATHR is in HLD during takeoff till 400ft AGL and i get a windshear in 200 ft AGL and pressing the TOGA buttons, nothing will happen right?
Are you not at TOGA already? What does QRH say you should do?