mathbionerd author Melissa Wilson Sayres has put together a nice animated explainer about how mtDNA coalescence happens and why mtDNA is not the complete picture of genetic variation: “Y and mtDNA are not Adam and Eve: Part 2 - What it means to be the Most Recent Common Ancestor”.
1. One person (or two people) did not have the ancestral state of all of our DNA. The person whose cells housed the common mtDNA ancestor (or Y ancestor) also had all of the other chromosomes (1-22 and X), but did not house the common ancestor of each of these chromosomes. These non-sex chromosomes are a lot more complicated. This touches on why it is also misleading to refer to the common ancestor of genetic "males" versus "females." Genetic females are not only their mtDNA - we also have 22 non-sex chromosomes, and two X chromosomes! Genetic males are not only their Y (and mtDNA), they also have 22 non-sex chromosomes and one X chromosome! Because the non-sex chromosomes (autosomes) can swap DNA, and are inherited through both the sperm and the egg, they much more complicated history than the Y and mtDNA.