This all seems right to me. As for your figured bass comment, you could have something like iii^6_4 for an e minor chord with the B in the bass, when the key is C major. But if you were writing it next to the staff you wouldn’t need to write the iii - it’s implied by the bass note and the figures, and classically figured bass writes the minimum it has to, for example just 6 instead of 63 for a first-inversion triad.
