On cleaning up the bottom of the tank, you can use a fish net to scoop things up or a turkey baster. I use a hand held battery powered vacuum cleaner and love it. Here's a link to it:
http://www.drsfostersmith.com/product/p ... &N=0&Nty=1
I don't know whether or not you'd be able to find something like this at a pet store but it sure is nice.
As you know, you can't really tell if the water is clean just by how it looks. Ammonia and nitrites can build up and these are both harmful but invisible. A functioning bio filter will neutralize these waste products but one of the reasons you test is to make sure your bio filter is functioning.
The byproduct of the breakdown of ammonia and nitrite is nitrate. Nitrate is also invisible and is not as detrimental as the other two (ammonia and nitrite) but it shouldn't be allowed to build up too high. The way to get rid of nitrate is to change the water. With a large aquarium most people do partial water changes every few weeks and only completely drain the tank monthly or even less often, assuming there's a good filter in place.