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P.S. I know not that much, just some basics, but this question really interested me :)
The mitochondrial genome has a nonzero mutation rate, though estimates differ according to method. Estimates are approximately 10^-8 per bp per year on average, and the mt genome is ~20,000 bp. So we can do some math and expect that many (or most) people experience heteroplasmy, which is to say that they carry various different mitochondria (in the same person).
Note also that you inherit multiple mitochondria from your mother, not just one.
So- no, not everyone has exactly the same mitochondria, even if we can trace them all back to a single hypothetical human.
The M.DNA mutates about 1% in a million years, and because our Mt-Eve is 150,000 years old, our mitochondria are 0.15% different, or 99.85% the same globally, and 99.95% the same in Eurasia.
The variation of mitochondrial DNA between different people can be used to estimate the time back to a common ancestor, because mitochondrial DNA accumulates mutations at the rate of approximately one every 3,500 years per nucleotide. They can measure the differences in a tree: