In the ST3 Browser, the triangular arrows pointing down or to the right are just buttons for collapsing / expanding the tree of instruments.
The first "Grand Piano 1 SE" (in
bold font) is the name of the branch in the Browser. The second "Grand Piano 1 SE" is the instrument itself. You'll see that I have some others too.
In ST3, the Disk Path should be "C:\Users\Desktop PC\Desktop\IRIG IK Multimedia\SampleTank 3 SE", that is the top-level one. And that folder should contain the "instruments" and "Samples" folders each with loads of files in them.
The path: C:\Users\Desktop PC\Desktop\IRIG IK Multimedia\SampleTank 3 SE is quite long but I would stick with it for the moment. It can be changed later.
For me the "Samples" folder should be in the same folder as "Instruments"; in your case that would be:
C:\Users\Desktop PC\Desktop\IRIG IK Multimedia\SampleTank 3 SE\Samples
but you have said that that folder is empty.
If you're feeling brave you could try this:
(a) make sure that you have all the Sounds Library download files somewhere safe,
(b) MOVE the files from "Sample Tank 3 SE/Instruments/samples" into "Sample Tank 3 SE/Samples",
(c) Start ST3 standalone program and set the Disk Path to:
"C:\Users\Desktop PC\Desktop\IRIG IK Multimedia\SampleTank 3 SE"
(d) rebuild the cache database (click the circular arrow at the bottom of the Browser),
(e) check that the (6?) instruments load and play OK.
Then report back. (I'm off to watch the 6 Nations Rugby on TV soon.)