I had received two traffic tickets. The first ticket was for going through the HOV lane w/o having more than one person in my car. The second ticket was for not paying attention and I got tagged for speeding. Do I have any hope of getting either of these dismissed? If I pay these tickets, will they affect my insurance rates since my insurance is in different state from the ticketed state?

read your policy risk factors or agreement. there you might get some points related to this.