No need to give yourself an ulcer, it sounds like Daz Studio (DS) doesn't know where the files are for some reason, the fact that it loads when using the Open with command or clicking the raw .duf file shows that its all in there somewhere. It's just a matter of connecting the dots within DS. It sounds like you have tried quite a few things but starting with the basics may help at this point since you have reached a deadend, just to make sure there isn't something small going wrong somewhere.

Ignore the data folder for the time being, what your missing is the connection between the Genesis 3 Female.duf within Studio and the file located on your hard drive which should be located on your hard drive at: (C:/Users/Public/Documents/My DAZ 3D Library) /People/Genesis 3 Female/Genesis3Female.duf

Okay so if there is nothing listed under the People/Genesis 3 Female Folder path within DS Content Library tab just to clarify do you mean there is no Genesis 3 Female folder at all in your content library or just nothing listed within that Genesis 3 Folder? Where does the folder path finish within DS? Or is it just an empty Genesis 3 Female folder?

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You need to make sure that two things are definitely matching. The install location on your hard drive and the Content Directory Manager Content Set. Check on your hard drive in explorer the location of your_ 'My Daz 3D Content Library'_ at the same path as above.

So it should be WhateverDrive/My DAZ 3D Library/People/Genesis 3 Female/Genesis 3 Female.duf

From here the files are either where they are meant to be which means Daz Studio has not been correctly configured to see your installed content at that location. If this is the case you need to use the drop down in the upper right corner on the Content Library and select Content Directory Manager. This Dialogue will show where Daz Studio is pointed to find your content this needs to match the installed path on your Hard drive.

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Or if the files cannot be located at the correct path, it may mean that something went wrong when they were installed. If you are using Daz Install Manager (DIM) please check and make sure the path is correct that your are installing to.

You can do this by selecting the cog wheel in the upper right corner of the DIM window. Selecting Installation and checking INSTALL path is correct here.

If none of this seems to help can you please post a few pictures for me, Firstly The Genesis 3 Female.duf file in the People folder in windows explorer or the finder window with the file path visible and also a picture of the Daz Studio Content Directory Manager showing the Daz Studio Formats Content Sets.

Hope this helps