Hi Oz29xr8!
You raise some great questions, which show that you're thinking about how to maximize your study time.
Should I only focus on the logical reasoning questions and reading comprehension passage types I struggled with the first time I took the LSAT? Ive been practicing all the question and passage types, but would it be best to focus on the ones I struggled with the most?
On the one hand, I wouldn't focus "only" on the type that you found most difficult. You should make sure that you are staying in practice with all question types. On the other, there is definitely value in focusing on problem areas, even if it's not exclusively so. So I'd certainly give special attention to those problematic areas, but don't completely ignore the other question types.
How can I improve my timing on both sections?
The first suggestion is to make sure that you're practicing under the real conditions of timing--it'll help your timing if you're regularly taking logical reasoning and reading comprehension sections and doing so within 35 minutes. If there are 25 questions in the section, that's about a minute and 24 seconds per question. When you're not taking full sections but are rather drilling yourself on particular question types, you can use that as a parameter for how long you should try to spend on a question.
Another suggestion is to keep your pen/pencil/highlighter moving. That definitely doesn't mean underlining everything you see, which then detracts from the usefulness of the underlining, which should be to spotlight certain aspects over others. Rather, you can scroll with your pen, moving it at a reasonable pace alongside the text to keep you moving through it rather than, for example, reading the same sentence over and over. While you're doing that, you can be sparingly marking up the stimulus or passage to make note of things like gaps in an argument, new terms introduced, a chronological order to events, and so on.
Lastly, when practicing logical reasoning questions should I focus on the most common question types that appear more frequently on the exam?
In general, it makes a lot of sense to focus on question types that appear more often than others. Yes, strengthen/weaken questions appear more often than main point questions, and must be true questions are the most frequent. If possible, though, I'd encourage you to make your way through all of PowerScore's materials. You'll find that there are many more must be true questions to practice than there are main point questions. If you worked your way through all the materials, you'd therefore be dedicating more time to must be true questions. But the same advice as I offered at the outset also applies here--you don't want to be completely out of practice with main point questions, so it's important to still be practicing them. There is a lot of value in focusing on problematic question types, but not to the complete exclusion of other types.