DON'T fill in the troughs until you know the source of the water. It may be seeping right through the block into the trough. In short, if you want to finish off the basement, you need to address the water issue. You may want to consider a sump pump anyway with a battery backup. These days, your insurance company will have a lot to say about what they'll cover, and not cover, in the basement - finished or not. With that in mind, assume that the water WILL rise up to the living space.
When you do re-frame out the area, you'll need to use pressure-treated lumber for the bottom plate. That way, if any moisture rises up from the floor, the PT wood can handle it. DON'T re-frame down into the trough, or even partially into it. Obviously, putting the bottom plate outside the confines of the trough will 'shrink' your room all that much but it's better than the alternatives. The 'smell' from the standing water and by framing in the trough will cause respiratory ailments to people sensitive to mold spores. This is all the more reason to 'collect' the water in a sump and pump it outside. That way, there's no standing water.