From all the photographs of various impluvia I've seen, they don't appear to be very deep -- practically wading pools, in fact. I could be wrong, but I don't imagine that there might have been too much difficulty in cleaning them, other than the fact that I suppose slaves would periodically have to scoop out stagnant water.
As caldrail has already pointed out, the slaves would have been quartered away from the family's rooms. I have a wonderful little book that I believe is now out of print, titled A Day in Old Rome by William Stearns Davis (Biblo and Tannen, 1972) that goes into a lot of detail regarding Roman day-to-day life. In the chapter titled "Roman Homes" there's a section devoted to the slaves' quarters, stating that the family slaves slept "in the very cramped barracks of the second story, a section of which looks down from an upper tier of columns above the court of the peristylium... For the slaves there is extremely little accommodation; any kind of a sleeping pocket, very truly called a 'cell' (cella) will answer, where a stool, a blanket, and a thin mat on the floor suffice for all save the upper servants."
Can't help with any information about any wide use of wooden partitions in Roman houses. But I do recommend this book by the late professor William Stearns Davis of the University of Minnesota, for an interesting and detailed look into Roman daily life in the year 134 C.E.
-- Nephele