Actually all your questions are answered by Shantideva.
It is impossible for this mind (consciousness) to see itself.
Just like your eyeball cannot see itself.
It was then argue what yogacara opponent, who said that mind is like the light. And the light illuminate itself.
This is rejected by Shantideva who said light doesn't illuminate itself, because light needs cause and condition.
The argument then goes on by yogacara who said that but it is the nature of light to illuminate.
This is counter over by Shantideva who said, in this case you shouldn't say that light illuminate itself, because light illuminate itself has a very different meaning with the nature of light is illuminating.
If you say light is illuminating by itself, it suggests illumination is independent of anything.
But if you say that the nature of light is illuminating, it doesn't suggest that illuminating doesn't need anything to illuminate.
The nature of light is of course illuminating, that is why it is called light.
Similarly, the nature of cognizance is of course cognize, that is why it is called cognizance.
However, it is indeed make nonsense to say that because of the mind, the mind has ability to see. Just like your eyeball cannot see itself, it is absurd to assert mind see itself.
But, it is indeed that nature of cognizant to just cognize, to just know, without an extra layer that control or see cognizance.
I am not here nor there.
I am not right nor wrong.
I do not exist neither non-exist.
I am not I nor non-I.
I am not in samsara nor nirvana.
To All Buddhas, I bow down for the teaching of emptiness. Thank You!