Is the controller working in the standalone version?
When using Spark as a plugin the connection is direct between the hardware and the software, it isn't routed via Cubase at all. That is how you are supposed to use the controller with Spark, so that you record your sequences inside Spark not on a midi track. You can drag the patterns out to a midi track from Spark after you have recorded them.
You should have 2 sets of midi ports listed, and it seems strange you only have the one set. Incidentally on windows they are not called Private but something like MIDI IN2(Spark Controller). The other set are for when you are using Spark as a general midi controller for something else, and you would route it inside Cubase the same way as any keyboard/controller, but you would not use this method for Spark. The 2 you have listed look like they are the general purpose midi set and so you would use these for controlling other software etc.. and should be enabled if you are going to do that. As long as Spark itself is seeing the hardware controller it doesn't matter that the private Ports aren't listed in your midi devices as you would have to disable them anyhow.
I would first run the standalone and make sure it is connecting to the controller and functioning correctly so that you at least know that Spark is seeing the hardware, it should happen automatically when you load it. The standalone takes away any DAW related possibilities to diagnnosing. The VST behaves the same way and should tell you if it can't connect. If it can't connect then you do have a problem.
As for audio, you don't need to record the audio, it's a VST Plugin so it will mixdown in the same way as all other VST plugins on audio export.
hope this helps!