Yes, they are a bit Rugby obsessed! Particularly in Y7. DS is not a rugby fan, that's the only bit he isn't as keen on, but there are lots of opportunities for other sports too.
DS is a lazy sod whenever he can get away with it and I have to nag him to do his homework. I know the boarders do their homework at a set time and there are staff there who can assist, which has to be an improvement on me attempting to help DS with his English homework while he grumbles that I don't know what I'm talking about (my degree was a waste of three years then)... So yes, they are definitely kept an eye on with regards to homework in the boarding houses. In fact, DS has joined them for homework time a few times now I think about it, as they run an after school club for day boys where they eat dinner, do their work and hang out with the boarders until parents pick them up. You can see what homework has been set and what's outstanding online too, so they can't really hide it if they haven't done what they are supposed to!
The boys are definitely pushed to achieve their potential on all fronts. There's a lot of encouragement to join in extracurricular stuff but the academic work is highly focussed on (I suppose you only have to look at their results to see that). I worried that would be stressful, but DS doesn't seem to be feeling under pressure with it all and he'd definitely complain if he was. I get the impression that boarders get a lot of focus and help - I suppose there aren't many of them, OFSTED rates the boarders separately I believe, so they really want the boys to do well! They will let you know quickly if there are any issues and in my own experience teachers seem very happy to discuss any problems or answer any queries thoroughly.
A friend of mine taught at LRGS for a term a couple of years ago. She'd been teaching in a very challenging inner city school beforehand and said that LRGS was the easiest teaching job she'd ever had! All the boys did as they were asked, first time, and were eager to learn and do well. How it compares to other boarding schools I don't know though.