As far as question #1, pre-trial diversion programs work very differently in different jurisdictions. If a pre-trial diversion doesn't require a guilty plea and any admissions, then it is not a convicton.
But on the other hand, if yours did, then it is a conviction according to the INS.
If it is a conviction, you have to look at USC 1182 as suggested by Mr. Knowitall and USC 1227 to see if your conviction qualified for any exceptions.

