I once reported the wrong number for a personal foul, I believe I reported 20 instead of 30. I noticed the fault after the ball was live again, then at the next dead ball I changed the number with the scorekeeper. This happened in the beginning of the game, so my question is:

Was I correct in how I handled the situation, or should I have done something different?

Also, what if this happened late in the game (doesn't have to be late in the game) and the player that committed the foul had 4 fouls and would be disqualified from the game with his 5th foul, but the wrong number was reported, allowing him to stay in the game. The fault wasn't noticed until the ball was live again with the player that should be disqualified still playing. What should be done in that situation given many different scenerios that could happen by anyone (the disqualified player included); someone scores, a foul, etc.

You can correct any number of a fouler if you have knowledge there was a mistake. That is usually difficult to find out all the time. When you know there was a mistake made, just get it corrected ASAP. The same goes if you fouled out a player. Correct the mistake ASAP. I would also make sure that I have a good pregame with the table personnel to cover these possible mistakes and if they have any questions from you to tell you immediately. Also many of these mistakes are made when you go too fast. If you take your time, you can make sure you have the right number and make sure you report the right number. Then you do not have to worry about what might happen in these situations. ;)

Peace

In the situation of the disqualified player still playing, once the error has been discovered can anything be done about it other than changing the foul and having him replaced?

no.

However, if you report 20 and should have reported 30 for his 5th foul, you'd better be damn sure when you go to make the change. Because it's probably gonna get ugly.