I enjoy it. Sometimes it can be a bit tedious, and some of the lecturers are as woefully uninspiring and useless as you could imagine. But many are quite good, and a lot of the work is interesting. Obviously it's very different to a-level maths. I find myself spending most of my time writing sentences rather than calculations in assignments, but that suits me as my verbal intelligence is probably my strongest..however I think the emphasis on proof and rigorous argument can perturb some people.
People work at different levels. Some barely pay attention and do a lot of recreational maths, finding the work rather trivial. Others struggle with most things. Others are somewhere in between. Many do assignments early, many leave assignments til the last minute.
Yes, it is fairly easy to keep up. I haven't missed an assignment yet, apart from when I just couldn't be bothered with a certain module.
I had an interview with Cambridge, but I did very poorly on the pre-interview test, for what reason I am not sure, as it was not really all that hard, but in any case, I was fittingly rejected. I go to Warwick and essentially an offer was immediate, as it often is; I then did just STEP I to get in, obtaining a 1, although a 2 would have sufficed (indeed, had I applied a year later and got the same A-level grades, STEP would have been entirely unnecessary, but I enjoyed taking it so no matter.)