Simple question that I can't find an answer to, can you delete rivers? Secondly, other than the visual issue, is there a reason rivers shouldn't be under lake/water tiles? It seems to be the only way to have a river coming out of a lake currently. 

You can delete sections of rivers by holding the right mouse button down and making a 'cutting' motion across the river.

If you click on the little question mark in the river menu, it'll pop up a box on the bottom right that gives some instruction, though it took me a bit of fiddling with it to get it right.