If you got a letter from the DA, then they have filed the case. It may not have made it's way into the court system yet and the date they gave you was premature. When the case comes on calendar, and you're not there, they will issue a warrant, which will cause you more problems. I would suggest you contact a local attorney there to check for you and make the appearances.
The reality of it is yes. Certainly they will need a reason to pull you over in the first place, and then they will have to suspect you have been drinking. They will find a reason and if you don't blow, you will lose your license with the DMV.
If you didn't plead guilty and you haven't had a trial, you haven't been convicted. If, in fact, they dismissed the case, or never filed, you should be able to find that out from the court itself. Just call the clerks office in Fresno. If there was some confusion, and they have filed, then there may be a warrant out for you to appear. Nothing but an arrest should be on your record.
That depends on a number of things. You will have to have someone look at the terms of your probation re alcohol, and the main term is obey all laws. I suspect a court will not like the fact that there was alcohol involved and could take a harsher view. you need to have an attorney look at this.