Under U.S. law, asylum may be granted to aliens who can establish they have well-founded fear of persecution if they were forced to return to country of citizenship or last habitual residence. The persecution must be on account of political opinion, race, religion, nationality, or membership in a particular social group. Typically, general conditions of unrest in a country are insufficient.
The answer depends upon many factors. It would depend upon whether you have been harmed in the past,...
I changed your question from the practice area of immigration to employment/labor. While you were working as a non-immigrant, your issue is not related to your status, but rather a employment/labor dispute.
I agree. DUI on and of itself is not sufficient to disqualify you for naturalization. At the same time, it might if it comes with a baggage. Please take you case for a very specific review with a good immigration attorney in California. At the very least, you owe it to yourself.