If I am not the file' owner or root, can I use chmod to change the file permission?
Assume I have group/write access to the file, e.g. 775
In a nutshell: No, you can't do that. Just for the plain reason that you could "steal" another user's file (related source):
Of course, only the owner of a file may use chmod to alter a file's permissions
There was another question on SO dealing with this here. The trick is to let
chmod check if you're in the same group or have enough permissions in order to change that file's ownership and then run it as
Basic answer is no, unless you have specific rights through the group you and the file is in.