1. Having a function doesn't prove reality. I can be scared out of my sleep by dreaming of being chased by a tiger. The tiger is not real, but has a function nonetheless, and like the cup is created by mind alone.
The tiger differs, in that it cannot leave bite marks on you. In that sense, it is not a fully functional tiger.
Still pain is subjective feeling, it is not a tiger. Bite marks are color or touch, subjectively created by eye-consciousness or body-consciousness. They are also not a tiger. The sight, sound, smell, taste, touch of a tiger is also subjective feeling, not objective reality. None of it is a tiger itself.
2. Other people share similar karma of human beings, but many people sharing the same dream does not make it reality.
This is no good at all, it sort of begs the question. My point is that the cup is not entirely a dream. If you assume the opposite, then of course all your arguments will then fall out nicely. But I ask you to demonstrate your premises, not assume them!
I've been demonstrating it with showing subjective feeling and never objective reality. If you can see that in your own case, then applying it to others should be the same. So, many people having a similar subjective dream does not make it objective reality.
3. When we think of the word "cup" each of us will have a basic image in our minds, but the shape, the color, the material will all be different. A particular cup in front of us will also change following our karma. We may know it as red, but if we were a dog it would be black and white. The sight, feeling, taste, texture and even sound of it heard when tapped is all dependent upon our own mind. The only experience of a cup one can have is through one's own mind. So we can never really say we've seen a cup itself, to be verifiable (because eyes only see color, and color is created by eye-consciousness. It is not external to mind, and it is not the cup). The same is applied to all ways in which we may say a cup is there.
I find this all quite true and beautiful. However it completely fails to address the point, which had to do with cups not spontaneously transforming into the Dalai Lama, as dreams are wont to do.
My point is that a cup is never a clearly defined static objective reality, and no one has ever had an experience of a cup itself, even in it's constantly changing forms.
4. False dependent origination is the coming together of illusory objects that depend on each other until they mutually fall apart. But each part is an illusion. True dependent origination is "All things in the three realms are created by mind alone", which is the ultimate truth that all things come from mind, which means they are emptiness. They are illusions and do not exist externally as though it may seem. So true dependent origination is directly pointing to emptiness. When you see emptiness you immediately see all things are created by mind alone, and when you see mind you see emptiness of all dharmas.
Well, I completely disagree with all this, in fact it looks crazy to me. The "mind only" idea is pure solipsism if you ask me.
Solipsism requires both objects and mind to be true, and all that is true. But if there is no object then there cannot be a subject. So obviously it is not the mind of materialists. It is neither nihilism nor solipsism. True mind, true dependent origination is beyond both extremes.
Emptiness cannot be brought in or left out. You can't pick it up or put it down. It has no name and no form. You can only awaken to it, or not.
Again, totally disagree. People ignore emptiness and speak conventionally all the time. I do it, you do it, nun, monks, and bodhisattvas do it, even the Buddha did it.
Right, we can speak conventionally all we want, but we cannot change the true nature of phenomena. Whether we realize it or not, we can't use words and concepts to change reality.
So you said valid and verifiable become iffy when emptiness is brought into the discussion. But valid and verifiable is always "iffy" when applied to phenomena whether or not we speak of emptiness. It is their true nature. We can speak conventionally while having correct view, or we can fool ourselves and just call it conventional speech while still holding false view of illusory objects truly existing as objective realities.