Didn't pay attention to this till I recently rewatched movie but find it odd that Brian is driving Dom's car to rescue him. Why not just put him in his own (new) ride and either allow Mia to be shown in Dom's car or just not have it in scene at all.
The Charger seems to be a popular fixture in these films. It would be more "cool", symbolic, epic, whatever to break Dom out of jail and put him behind the wheel of it upon freedom. The two have been repaying each other with 10 sec cars through out the series.
Guess I can buy that ~ "Friendship/payback" deal but still figured it would have been also symbolic 2 showcase Mia (family) driving it up to present it for him. But that is of course my own opinion.
If the "family" relationship between Mia and Dom were greater then the bromance between Dom and Brian I would agree, but it isn't. Here is the hierarchy of relationships in the series:
1. Dom and Brian
2. Dom and Letty
3. Brian and Mia, which of course moves up now that Letty is gone.
Are we to assume that it is the same charger? How could Brian have fixed it in time? I know we don't see a time elapsed between Dom being sentenced and being shipped to the prison, but we can probably assume it wasn't very long. I know that sometimes transferring inmates takes forever but still. The car was probably totaled when it got exploded in the tunnel.
As far as why Mia wasn't driving it. Nothing sexist here but, I don't think she could of handled it. Dom could barely handle it, how is Mia supposed to? But for flow of the movie I would assume that it is just representing that Brian fixed it as a way to be on his good graces. Someone else already discussed that though so I wont go into any more detail.