I have a problem with my fresh Debian installation. I cannot write on any USB stick.

Does your USB flash drive seem to be write protected and read only after a new installation of Debian? Please check if you have the following two lines in /etc/fstab:

/dev/sdb1       /media/usb0     auto    rw,user,noauto  0       0 /dev/sdb2       /media/usb1     auto    rw,user,noauto  0       0

If yes, remove them and you should be able to write on USB sticks again with your normal user account.