1. Is vipassana the tranquil mind?
Vipassana is insight, which can be achieved through vipassana meditation.
Samatha is tranquility, which can be achieved through samatha meditation.
Thus, vipassana is not the tranquil mind, but samatha meditation can lead to a tranquil mind.
"These two qualities have a share in clear knowing. Which two? Tranquillity (samatha) & insight (vipassana).
When tranquillity is developed, what purpose does it serve? The mind
is developed. And when the mind is developed, what purpose does it
serve? Passion is abandoned.
When insight is developed, what purpose does it serve? Discernment is
developed. And when discernment is developed, what purpose does it
serve? Ignorance is abandoned."
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(Vijja-bhagiya Sutta)
2. Does the tranquil mind observe before the arising of consciousness?
Consciousness arises before name-&-form (nama-rupa), which are mental and physical phenomena. Thus, the tranquil mind would not observe before the arising of consciousness; consciousness would arise first, then the tranquil mind would observe.
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"And what is dependent co-arising? From ignorance as a requisite condition come fabrications. From fabrications as a requisite condition comes consciousness. From consciousness as a requisite condition comes name-&-form. From name-&-form as a requisite condition come the six sense media. From the six sense media as a requisite condition comes contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of stress & suffering.
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And what is name-&-form? Feeling, perception, intention, contact, & attention: This is called name. The four great elements, and the form dependent on the four great elements: This is called form. This name & this form are called name-&-form."
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(Paticca-samuppada-vibhanga Sutta)
3. What is meant by dualizing the self?
There is no self in the first place because of impermanence. Thus, no self can be dualized.
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"Bhikkhus, how do you conceive it: is form permanent or impermanent?" — "Impermanent, venerable Sir." — "Now is what is impermanent painful or pleasant?" — "Painful, venerable Sir." — "Now is what is impermanent, what is painful since subject to change, fit to be regarded thus: 'This is mine, this is I, this is my self'"? — "No, venerable sir."
"Is feeling permanent or impermanent?...
"Is perception permanent or impermanent?...
"Are determinations permanent or impermanent?...
"Is consciousness permanent or impermanent?" — "Impermanent, venerable
sir." — "Now is what is impermanent pleasant or painful?" — "Painful,
venerable sir." — "Now is what is impermanent, what is painful since
subject to change, fit to be regarded thus: 'This is mine, this is I,
this is my self'"? — "No, venerable sir."
...
(Anatta-lakkhana Sutta)
4. How does the tranquil mind dualize the self?
There is no self to dualize (refer back to my previous answer to question number 3). Thus, the tranquil mind does not dualize the self.
5. How does the dualized self stop emotions not ruling the mind?
There is no self, and therefore no dualized self (refer back to my previous answer to question number 3). Thus, there is no dualized self to do such.
-Apannaka
