Assuming I am right about the first part of this question....

Two outs in the inning and a runner reaches on an error. If he scores and anyone after him in the inning, those runs are UNearned, right?

Okay, now say you change pitchers after that 2-out error. The new pitcher gives up several hits/walks allowing not only the inherited runner to score but also his runners.

Are any of those later runs earned?

Any runs scoring after what should have been the third out are unearned to the pitcher who was in the game at the time of the botched 3d out, and to the team.

If a reliever enters and lets inherited runners score, those runs are charged to the prior pitcher but are unearned. But if the reliever puts on new baserunners (batters he faced), and if they subsequently score, those runs are charged to him, and they are earned to him, even though they are unearned in the team stats.

For this reason it is possible that in your team stats, you will show fewer earned runs in the team totals than if you add up all the pitchers' individual numbers.

Perfect. Thank you.