I'd say it's better to inform them rather than not since I believe you'd need to for the bar. For the speeding ticket, make sure you know the date and other specific details. The addendum for that can be pretty short I believe, just a quick explanation of what you did to get the ticket and what you did to rectify the situation. Better safe the sorry ya know.
Do it immediately and explain why you didn't send it originally in the addendum as well. Make sure you know the date and all the other important details (ticket number, fine amount, etc) as well since they will likely want it. Plus you will need it when you apply for the bar, so it's a good idea to have a record of that for later.
I got some advice a few months back that really shifted how I viewed this test for the better. We put a lot of pressure on ourselves to do amazingly well on this test and sure, that's for a good reason, but it is also often our downfall. In putting so much pressure on ourselves we make it harder to do well. At the end of the day, we are going to take the test and get a score. Maybe we will be happy about it, maybe not. But allowing ourselves to get greatly upset over a number is not worth it. Schools do consider other factors when reviewing applications. The LSAT is important but it's not everything. So try your best on the LSAT. But whatever the outcome, be proud of how far you've come and how hard you worked to get that score. If you can shift your perspective to be more appreciative of the work you've put in and the progress you've made, the test because less frightening and less difficult. I know I personally found it easier after I began to put less pressure on myself. So, I hope this helps you too. You've made such incredible improvements and that is worth being proud of. Take a breath and keep working but with the intention of simply trying to be better for the fun of it rather than viewing your progress as though it isn't good enough.
I think it depends how confident you are about your ability to get your goal score in April. Remember there's no need to rush to take the test. We put a lot of pressure on ourselves to take the LSAT that a lot of the time we push ourselves to do it before we're ready. If you take PTs and aren't in a spot where you feel you can get your goal score for April maybe just wait to take the exam in June. That way you can focus on drills and leave the PTs for the last few weeks before the exam. If you're confident about taking it in April then doing a PT once a week is a good idea. Doing weekly tests helps to build stamina and familiarity, especially if you do it roughly on the same day and time as you plan to take the real one. You can also always retake old PTs because odds are you won't remember the answers to the questions if it's been a few months since you last took them. Ultimately, you want to take the LSAT at a time when you feel confident you can tackle it. Don't feel you have to rush to take it. Determine how close you are to your goal score and what you need to work on to get there (timing, stamina, specific question types, etc). That will help you figure out how to prepare.
Currently stuck in the mid 150s on my timed PTs but get high 160s/low 170s during blind review (I only spend about an hour extra on blind review). Any tips to help with timing since that seems to be my biggest issue right now? Been stuck here for months now and it's really upsetting.
Like the other people said, check the guidelines for the schools you want to apply for. If you aren't able to take the April LSAT for the schools you want to apply to and are truly unhappy with your Jan. LSAT, I'd say consider a gap year. Take some time to study more, maybe even take a slightly later LSAT. You can still work on your essays and apply at an earlier point next cycle.