Well, first of all, thank you all of you for your suggestions.
As for user rights, it would stay just the same, because of the server software limitations; there is no option about that. I have sent an e-mail to my hosting company and they said me "You can select a specific folder that an FTP user can access, but cannot change permissions for what they can do in the folder as an FTP user." In this case, I am not to be able to do anything about that, sorry.
Here is my suggestion:
Let us say, there is a thread called "FTP Uploads" here and then a user would like to upload any file(s); He or She would post there and moderators says okay or not. Thus, all of us know who uploaded which file. Each user will uploads to their folders and moderators will move to right place later. Whatever.
A second option; we will shut down the FTP and build a new "user login based file management web site".