Data on file exchange partition is owned by 1000 and locked. How can I unlock this in OS X?
Unlocking the file
You can unlock files from within the terminal using the chflags command with nouchg:
sudo chflags -R nouchg Bilder

According to the man page for chflags:

uchg is the user immutable flag
no in front of a flag removes the flag: nouchg

Preventing this from happening in the future
A general solution would probably be to avoid handling permission altogether and using NTFS or FAT for an exchange partition.
However, I specifically voided such a solution (FAT32) this time, because I encountered serious errors the last time.