I would love to check it out when new spots are available!

Hard to say, really. I would suggest you focus less on your score trend because it will naturally fluctuate. Instead, focus on making small improvements over time. The Japanese have a word for it, Kaizen. It is a great philosophy for life in general, but it comes especially in handy when studying for the LSAT. You may not see a score improvement but every time you sit and drill or take a timed section or preptest, you are making a small improvement in your overall LSAT ability. Over time, that will become apparent to you as you will see your scores improve eventually, as long you study with the right mindset and thoroughly review all of your mistakes.

Everyone is different, so I wouldn't worry about it too much. The best thing for you to focus on right now is to learn the basics of this test and get good and really understand what is going on in each question. The LSAT is a reading comprehension test first and foremost so get used to reading to understand. Worrying about what score to expect or how fast it increases is a distraction, I know because I used to do the same thing.