In general in the US, a non-lawyer cannot own a law firm. It violates professional rules of ethics prohibiting the splitting or sharing of legal fees with someone who is a non-lawyer. Check WA laws to be certain.
Need more clarification. Were you convicted, or was someone else? Who are you trying to sue? (i.e. were you convicted and trying to sue the DA, or are you injured and trying to sue the person who hurt you & got the DUI?)
In order to sue someone (and win) in civil court, you have to show that you were damaged, and that it was their fault (through deliberate actions or negligence). If the person you are suing was convicted of a DUI, that's probably going to help you, as a criminal charge (such as DUI) carries a higher burden of proof than a civil trial.
Find a good personal injury lawyer and talk to them. Usually, the initial consultation is free, and they are paid on a contingency (like, 30% of whatever you recover + expenses). A contingency lawyer genrally won't take a case unless he/she feels he can win, because if you don't win, they don't get paid. So it doesn't hurt to talk to them.
Yes, find a good personal injury attourney. Not necessarily one that advertises on TV. The link above is probably a good one. Check with your local bar association for one certified in that practice. Also see if there is a referral list from someone you trust -- in Houston and Colorado you can use referrallist.com, a radio host/consumer advocate website.