From my current understanding this is how I see it.
Firstly, I need to explain the average run-of-the-mill mind...
In Mahayana what defines a person is ego. In its most simplistic terms ego is a collection of thoughts and feelings that cause one to lurch aimlessly towards various degrees of pleasure and retract from various degrees of pain. It is a reactive measure that aims to create a sense of safety and security. These very acts of aversion and attraction give the sense that we are in control, that the decisions we are making are individualized, personal and contribute to our wellbeing.
The truth is that all those feelings, thoughts, aversions and attractions centre around the characterization of worldly perceptions shrunk into a singularity called [insert name here]. That is to say, they have arisen in dependence upon whatever has been perceived, but then mistaken itself as existing in conflict to the world it lives within; the very world ego gathered its characterization from. By isolating oneself from the world in this way, suffering endures. This is called ignorance or to use a more user-friendly term not seeing clearly.
With the above in mind, when we act as if each person has his or her own consciousness, sensation, and thoughts, there are two things happening...
That they are actually already free from ego and suffering. They have Buddha nature right now. Sunyata.
But yet they are ignorant: not seeing what is right before them. The recognition of this is a recognition of an independent consciousness or ignorance. You cannot ignore ignorance or else there would be no compassion, and thus you couldn't give a teaching or help in other ways.
Just to make this somewhat paradoxical point more prominent, chapter 17 of the Diamond Sutra might help neutralize the dissonance that occurs from that paradox, but understand that the teaching is the recognition of ignorance and where it points is sunyata; they are seemingly one and the same.
“Subhuti, it is just the same when a disciple speaks of liberating
numberless sentient beings. If they have in mind any arbitrary
conception of sentient beings or of definite numbers, then they are
unworthy of being called a disciple. Subhuti, my teachings reveal that
even such a thing as is called a ‘disciple’ is non-existent.
Furthermore, there is really nothing for a disciple to liberate.”
“A true disciple knows that there is no such thing as a self, a
person, a living being, or a universal self. A true disciple knows
that all things are devoid of selfhood, devoid of any separate
This moves us nicely onto your last point: it is not that Mahayana believes that all is a projection of mind, but that all perceptions operate in unison with the world and that there cannot be personal decisions made on the basis of the incalculable processes currently at play. There is no special character in the middle of it all. All is what is.
If you had said, "but I made a decision to upload this question". That is absurd! Think about all the necessary requirements that were needed for you to type and upload this question: the computer and it's components, electricity, internet, your mother and father... You made no decision, it just happened in dependence on other factors.
In this way, sunyata is how we come to understand the emptiness of how we erroneously characterize ourselves, and we see the sheer complexity and utter simplicity of it all in a single moment called the here-and-now.