If you are using Windows (and probably Mac too) all these options are there. Just not in Limewire. Highlight a file in your shared library and press explore, then the folder containing your downloaded files will appear. In there you can organise, see last date modified and everything else in your request.

In Limewire Tools-->Options-->Saving you have the choice to specify which folder you want specific filetypes to be stored (not by genre though)

Maybe having some of these things in Limewire would be handy, but there are much more needed options that need looking into right away.