CHMOD which is used to change permissions via FTP is a UNix command and does not work with Windows IIS.
What you see in FileZilla in your image using CHMOD means nothing as FileZilla is not able to read the permissions on the Windows IIS box. Which is also why you can not use FileZilla to set the permissions.
CHMOD 755 to 644 are Unix permissions and have nothing to do with Windows IIS. In Windows the server admin has to set, Read, Wite, and Modify permissions on a directory for the IUSR account that the website runs under.
This is all quite basic stuff for a web host and that fact that your web host is referring to Unix permissions (access codes though (ie from 755 to 644) those cannot be changed) means that they are completely clueless as to how to run a Windows box.
I suspect that this lack of knowledge means you must be using a host is is a reseller for another company. This will also explain why your host is unable to help you.
I would suggest that you move web host as the replies they have given clearly show they have a lack of understanding of a Windows Hosting environment and should not be trusted to host a Windows website.