what version of Kontakt player do you have? If it’s Kontakt 5 then the Komplete 9 install will simply replace your current player version by the full version. All Cubase projects that used an instance of Kontakt Player will still work as before, you’ll just get a full Kontakt instance instead of a Player.
(EDIT: this is only true of course if you install the plugins into the same folder as where the player was installed. but I don’t know what happens if you install it into another folder)
If your current version is Player 4 or below, then the Komplete 9 installer will leave that old version alone, nothing will be replaced or deleted. You could decide to uninstall the Player V4 BUT: every Cubase project that used an instance of Kontakt 4 will show a “missing” plugin, because it treats Kontakt 4 and 5 as different plugins, it doesn’t know that Kontakt5 is an upgrade of Kontakt4. And if the plugin is missing, you can’t see anymore what library or patch you were using in that project… So you have the choice of either accumulating old versions of NI-plugins (because it’s the same for Battery, Guitar Rig, Absynth, …) on your PC, or going through every Cubase project after the Komplete 9 install, replacing every Kontakt 4 instance by the 5 version, and only then uninstalling V4.
Which is what I’ve been doing the last 2 weeks BTW: opening some 40 projects, replacing all Kontakt 4’s by 5’s, Guitar Rig 4’s by 5’s, etc, and while I’m busy, replacing all HalionOne instances by HalionSonicSE’s (yes, Steinberg does this too…), Ultra Analog VA-1’s by Ultra Analog VA-2’s (yes, Applied Acoustic Systems does this too…).
I don’t know why you’re not seeing the Kontakt Factory Library though… There’s an “add library” button on top of that left side library navigator, where you can point Kontakt to the location on your harddisk where the library is installed, did you try that?