Regarding your initial questions, a helpful metaphor is a series of mirrors. Suppose you see an image in a mirror. You check where the reflection leads to find another mirror, in which the image is also reflected. You continue on and on, but keep finding mirrors with images rather than the actual thing. But at some point the actual thing has to be there to produce the image in the first place. In short, a regress is either vicious, or it is not. A vicious regress, if it continues to infinity, is ungrounded. (One could also have a vicious circularity.) Aquinas’s First and Second Ways essentially claim that causation generates vicious regresses, necessitating a first mover or uncaused cause.
Uniqueness of the uncaused cause is posterior to the demonstration. The Thomist arguments purport to show that there exists at least one purely actual uncaused cause. Suppose there exists another purely actual uncaused cause. Then, in order to be distinct, it must have some property that the other does not have (or the other has some property that it does not have). But neither can have any potentiality relative to the other, so they must be the same.
It could start from any singular instance of change (or any substance that has an efficient cause, or what have you). But in order to argue for the necessity of an unmoved mover or uncaused cause, you would have to sustain the claim that each subsequent change has a cause/each efficient cause itself has an efficient cause. Otherwise, you would not necessarily generate a vicious regress.