Thanks for the tip.
I have created special user for the backups.
Just checked the admin user and the same thing. SSH ok, directories created, no files transferred with error "module is readonly".
root user can't log in via SSH. His home directory is /root. I'm afraid if changing it will not break my DSM and I don't want to store backups there.
Checked chmods, checked home directories permission and seems to be ok there. I have no idea what is going on.
PS. Chmod 755 and chown to admin on cwp_remote directory didn't helped.