Does every mitochondrion in a cell contain the same DNA?
This link seems to have good information that answers most of your questions.

In my mind, there are two types of mitochondria: ones that work and ones that don't. Mitochondria do have DNA but that mDNA is there to encode proteins for their specific functions (e.g. to create ATP). So, although the mDNA may not be uniform for every mitochondrion in your body, it is most likely functional unless you have a mitochondrial disease. If you do have a mitochondrial disease then it suggests that some of your mitochondria are functional and some are not (otherwise you would be inviable).

As discussed in the comments, all DNA undergoes mutations so that even identical mDNA genomes may vary after undergoing some mutations. It's possible that only one genetic line of mitochondria was passed to you from your mom. In this case all the mitochondria in your body would be identical (except for minor mutations). It's also possible that your mom inherited and passed on to you more than one genetic line (as is the case in viable mitochondrial disease).

Mitochondrial repair mechanisms do exist but they differ in various ways from nuclear DNA repair and may be more prone to damage.