Auto insurance

Hi, I moved to the US a year ago, I live in PA and have already had several incidents with my car and insurance. 1) I got into an accident while driving on a slippery road in winter, the insurance covered it but it went up in price sharply. 2) The insurance did not notify penndot that we had insurance, so we were officially driving without insurance but we had an insurance ID. Of course, we did not know about it and our registration was suspended and you wrote a fine of $ 245, a court date was set for October. 3) Yesterday I was driving on the highway and it so happened that I exceeded the speed limit from 70 to 90. I received a fine of $ 171. Please, what should I do in the third case? Do I need to pay the fine right away or is it better to go to court? And how much will the insurance go up in price in my case? Now I pay $ 250 for 1 car. When will they update the database or will this fine remain in my history forever?