^ Outside of a few specialized LLM programs law schools don't really specalize and employers certainly don't say oh, I want x-type lawyer from school A and y-type lawyer from school B. Law school is a general education, get the best one that fits with your finances, numbers and geographic restrictions. If you end up stuck between two schools then see which has the strongest faculty in your area of interest. HLS has some really good things going on with international law.
5hrs a week isn't a lot - put in some serious time every week, lots of practice and make sure to review all questions you get wrong so you know where you went wrong, and I think you'll improve a fair bit still. Speed in the games comes with practice. Accuracy in the rest comes down to understanding how the questions work. After a reasonable bit of study and practice I rarely ever got LR or RC questions wrong. I never did get quite quick enough at games to finish them all, but rarely got any I did finish wrong - end result was good enough to go anywhere I wanted. I was testing about like you about this far out.
I'd say do your best in college, study for a degree that is marketable in and of itself and think about law school in three years. For now you need to work on self discipline/self motivation. A top law school is wayyyy harder than undergrad. I almost always had the highest grade in my class in college and usually without really trying terribly hard. I worked very hard in law school and was still not the top in my class. Being an actual lawyer is harder still, at least from a motivation standpoint (way more boring than law school, but not necessarily more challenging). If you can't make yourself go to class and study are you sure you want to review documents and write tedious memos 90 hrs a week?
I don't know anything about Oregon, but Colorado is a good school, Boulder is fun (but a bit wacky in that liberal-college-town sort of way) and Denver is fun and not wacky (and not far away). There isn't a better place in the states for outdoor fun (rockclimbing, biking of all types etc).
That's a tough one - I think I'd go with the full ride at UCLA, but I don't care for NYC so for me it'd be down to Chicago and UCLA. Chicago has an excellent academic program and is particularly strong in law and economics. My not-all-that-well-informed guess is that Chicago would give you a modestly better education than the others, but they are all just fine.
All will give you a shot at big law, but none will guarantee it. I know a few recent NYU and Columbia grads with no jobs and with jobs at some of the nations top firms. My guess is that on the east coast NYU, Columbia and Chicago are about even with UCLA lagging a bit. I'm not really up on west-coast hiring practices, but my guess is that UCLA would do just dandy.