That sounds like the expnungement paper from the court. What is more important is what your criminal record looks like. An expungement doesn't clear your record. What it does is withdraw your plea and dismisses your case. This allows you to answer "never been convicted of a crime" when asked by a private employer. Your rap sheet will show that the case was dismissed but the arrest will still be on your arrest record, If you want to check to see what your CA criminal record looks like go to the CA department of justice web site and click on thier link for "criminal record request" send them app $15 and your live scan fingerprints and they will send you a copy of your criminal record.
Yes,it sounds like it but you would need a copy of your record to be certain. You don't say what your sentence was etc.
From my reading of your question, it sounds like you may not have received an expungement of your record and you may be right to question what you did receive in the mail. I would suggest you speak with your lawyer to get clarity. #1 it sounds like the court just sent you a certified copy of the minute order showing that your case was dismissed after you completed your program. That means you no longer have a conviction on your record, but the fact that you were arrested and charged remains on your RAP sheet. The only way to get that removed is to bring a motion to court or have the police department to agree to destroy all records of your arrest due to your factual innocence of the charges. You may want to look at PC section 851 for more details.
It does not seem to me however that you were factually innocent of the charges or you wouldn't have entered a conditional plea and attended the program. So it may be that your attorney did all he could for you in the end. You had the case dismissed you can say you were not convicted of the charge, but unless you can prove you were factually innocent you will not have standing to have the arrest record or reports of your arrest destroyed. I hope that gives you a better understanding based upon what I perceive your situation to be.