Not really. There's a hundred of them. A whole bunch of candidates that are at the borderline and are ancestors of every member of the species.

As an extension of that fact, if there was a single true Eve the population would be at extremely high risk for genetic defects.

It's called a population bottleneck, where a near extinction event forces almost all individuals to share a large proportion of their genetic material, and the most recognizable example is in cheetahs.

http://cheetah.org/about-the-cheetah/genetic-diversity/

Nope. Any two organisms have a unique MCRA of either gender. https://en.m.wikipedia.org/wiki/Mitochondrial_Eve

That is a very specific thing.

It only applies to mitochondria, not the genes in the nucleus or anything constructed from those genes.

It's only unique because the "MR" in MRCA stands for "most recent".

You could have a species that's a million years old with an MRCA that's only 500 years old. You could also have a species with no MRCA. (As in, the only way to find an MRCA is to trace back into ancestor species.) Picture two islands where only males travel between them.

Mitochondrial Eve is the most recent common ancestor of our mitochondria. But that only tracks purely mother-to-mother descent; there could be a more recent female common ancestor.

Consider the hypothetical population consisting of two people, whose fathers were both first cousins and whose mothers are second cousins, on their mother's... side.

Their mitochondrial MRCA is their great-great-grandmother on their mother's side, but their MRCA's are their great-grandmother (and great-grandfather) on their father's side.

The entire human family tree is like that, but way, way more complicated.