As noted by depperm, the official answer to several of these questions is "this has not been revealed". I would, however, like to examine some of what has been revealed, in order to narrow down the possibilities.
As Joseph Smith taught:
you must begin with the first, and go on until you learn all the principles of exaltation. But it will be a great while after you have passed through the veil [died] before you will have learned them. It is not all to be comprehended in this world; it will be a great work to learn our salvation and exaltation even beyond the grave (source)
Question 0: According to LDS is there a fixed and finite number of human beings?
This is not a teaching of the Church of Jesus Christ of Latter-day Saints, and there is no reason given to believe that God's direct posterity is capped. Moses 1:4, 39 certainly imply that God's direct posterity is endless:
4 And, behold, thou art my son; wherefore look, and I will show thee the workmanship of mine hands; but not all, for my works are without end, and also my words, for they never cease.
39 For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man.
If God's work is bringing about immortality & eternal life for man, and His work is without end, that suggests to me that He will not run out of people to bless in this work.
The Doctrine and Covenants Instructor's Guide, the Eternal Marriage Student Manual, and the Gospel Principles Manual speak of the concept of posterity in the eternities using the terminology "eternal increase".
Question 1: The origin of the view that there was never a point where we did not exist. We grow & develop, but do not begin or cease to exist
This is established in multiple places; here are some examples:
Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be. (Doctrine & Covenants 93:29; compare Abraham 3:22-23 for greater insight on the terminology)
Now, repentance could not come unto men except there were a punishment, which also was eternal as the life of the soul should be, affixed opposite to the plan of happiness, which was as eternal also as the life of the soul. (Alma 42:16)
Question 2: Does this belief indicate the eternal existence of each specific, individual human being or some sort of notional existence of each or of mankind as a whole?
The pre-mortal, non-notional existence of individuals is clearly taught in Abraham 3:22-26 and Alma 13:3-5; the information we have on the nature of intelligences is limited, but what is known clearly implies individuality.
Question 2a Prior to birth on earth is each human being spirit only?
Intelligence + spirit is suggested by Abraham 3:22-23. From The Guide to the Scriptures:
The scriptures also may speak of intelligence as referring to the spirit element that existed before we were begotten as spirit children.
The sequence of development, then, would be:
Intelligence => Spirit housing our intelligence => Physical body housing our spirit
Question 3 If so, was there a fixed and finite number of spirit human beings in existence prior to creation?
Not necessarily. Joseph Smith taught that God has created multiple worlds and His children are not limited only to this one:
22 And now, after the many testimonies which have been given of him,
this is the testimony, last of all, which we give of him: That he
23 For we saw him, even on the right hand of God; and we heard the
voice bearing record that he is the Only Begotten of the Father—
24 That by him, and through him, and of him, the worlds are and were
created, and the inhabitants thereof are begotten sons and daughters
unto God. (Doctrine & Covenants 76:22-24)
Therefore, even if we accept (for sake of argument) that all spirit children of God who would live on this earth already existed in spirit form prior to the creation of this earth, it would not mean that there is or was a finite number of God's spirit children.
(Whether or not the council in heaven occurred in multiple sessions is unclear--as is the function of time outside of mortality)
Question 3a If so, does depleting this number through the process of birth on earth usher in the end of the age?
No, children will continue to be born after the second coming, during the Millennium:
And the earth shall be given unto them for an inheritance; and they shall multiply and wax strong, and their children shall grow up without sin unto salvation. (Doctrine & Covenants 45:58)
Question 3b If not, does the end of the age leave some number of human beings bereft of a body for the rest of eternity?
No, see discussion of multiple worlds under question 3.
I recognize that these concepts make many uncomfortable, and that Latter-day Saints have a distinct view of what is meant by Biblical phrases such as "let us make man in our image", "joint-heirs with Christ", "the measure of the stature of the fulness of Christ", "we shall be like him", and others.
It is not my intent to offend but to explain what I believe. I believe that God can make us as He is. When asked if God could really exalt His children in this way, I am inclined to quote Phil Matheson who stated: Yes, our God is so grand.
Disclaimer: I have drawn inferences that I believe are reasonable from what God has revealed, but these thoughts are products of my own study and do not constitute official statements by The Church of Jesus Christ of Latter-day Saints