1. I've tried to catch up using E&Es but they've been inadequate. For example, Glannon's E&E for CivPro is universally recommended but doesn't even mention opportunity to be heard, unless it's in the actual E&E sections which I haven't gotten to yet. Should I also get a "here's what the law is" treatise like Chemerinsky to keep up throughout the semester, then use E&Es to do well on the finals? Or am I basically screwed if I don't read the casebook for 1L classes?
2. Visiting profs--I figure I'll never see them again or ask them for recommendations so is "cultivating relationships" with them basically pointless too?
Depends on what you need a recommender for. If it's a clerkship you're after you'll need an HLS prof. If you want to add someone to a list of references to give to firms/summer internships, a visiting prof is often quite willing to be listed.
4. LRW isn't blind, so should I avoid being seen as the person who bickers over grade technicalities? ("well technically this component has no weight so how can there be a penalty against something that has no weight"). In undergrad my grades were usually unambiguously one thing or another so I never really waved the syllabus because I figured I had more to lose by making a bad impression on the prof.
Yes. Were you planning on turning in a terrible draft and telling the Climenko that it doesn't count toward your grade anyway in conference? That would be a bad idea.