I was banned on Psn for 7 days for nothing.
so I can't log in and play MW Warzone, but I know the Activision data from the banned PSN acc. When I register the Activision Acc on the 2.acc, my progress is transferred to my 2.acc, for example things that I bought ingame, level etc?
No, why should it?
If you really got banned for nothing, go to support!