Let's cover your experiences thus far so I don't overlook the obvious...
1. You have a registered/licensed/activated copy of Kontakt 3- which you have run on its own and opened sounds from it's library. Thus found the samples/sounds in those folders called Synth, Band etc....
2. (Not really pertinent, but proves everything is working..) Kontakt 3 scanned your computer and built its own database taking note of all the files on your computer it can read...
3. When you started KORE 2 after that, it paused on start and said it was registering Plug-ins.
4. After starting KORE 2...You highlighted the little picture of an vertical electric outlet Plug (universal symbol for Plug-In). You saw a field for Internal and VST.
5. You highlighted
VST and
Native Instruments which then put on the far left side a listing of all your NI stuff. You double clicked Kontakt 3. You then clicked the EDIT button right below the 0 KORE Logo.
6. You now have a new window running Kontakt 3. You clicked on FILES in that window and navigated to that same folder with Synth, Classical, Band etc...and NO SOUNDS SHOWED UP?
7. If sounds show up and you can open the presets then everything has been working fine from the start. If sounds do not show up then something is wrong in one of the previous steps or you skipped something or didn't fully grasp the manual or tutorial videos.
8. On a note for workflow- you should not want to IMPORT YOUR KONTAKT 3 library into KORE. That defeats the purpose and you would be back to surfing another million presets. You want to extract the best of Kontakt and FILE THOSE SOUNDS as Kore 2 sounds and save them with keywords. In other words, you save the preset as you see fit and YOU decide the categories/description.
That's the general idea behind a "Best R&B Leads" submenu of presets.
It would conatin Leads from Massive, FM8, Kontakt, FreeVST, KVRcrap, internetjunk, homiessamples, vstonlyyouhaveeverheardof, etc...