Hi Felix!
LR can be challenging and has a lot of moving parts. There is the time issue related to understanding, but also related to difficulty. You need to know where you are at in the section and whether an intuitive approach or a more technical approach is more appropriate. Early in the section, trust your gut and move quickly. Later in the section, be more cautious and reason things through.
There are three things that you really need to accomplish in LR:
1. Understand the task, as defined by the question type.
2. Develop a familiarity for which argument structures are likely to appear in which question types. (Ex: where do issues of causation most likely come up, or conditionality, etc.)
3. Keep in mind the most common ways of developing incorrect answers in each of the various question types. (Ex: answer choices that are too strong are a frequent incorrect, yet tempting incorrect answer on Must be True questions, or answer choices that are too weak and therefor consistent with the original argument can often be tempting on Strengthen/Weaken questions)
If you have a good sense for these three tasks, LR will start to fall into place.
You had two questions though that I'd like to deal with directly. First, with regard to conditional logic, it is all over the LR section, mostly in the following question types:
Must be True / Most Strongly Supported
Must be False
Sufficient Assumption
Match the Reasoning/Flaw
Principles
Make using notational systems something you are comfortable with and your life will be so much easier. Here's a set of language cues you can use to organize statements into their sufficient and necessary conditions.
With regard to abstraction, pause as you read through the abstract answer choices and relate their individual pieces back to specific parts of the argument as you read. So when the argument refers to "a phenomenon" or "a behavior" make sure before you continue reading you know what that refers to. if you go piece by piece, the meaning is more readily apparent.
Hope that helps and good luck!