Let me work through some of your questions:
Any files you have shared are available for others to download from you (including incompleted files), if you dont wish this to be the case use a different folder for incoming files than those holding the files you wish to share, this option can be found in Settings->File Transfers , look at the top of the left pane and change the folder there.
You can edit your library to ensure no incompleted files are shared in the normal "Library " button along the top of the client.
If you have incompleted files still showing in the "Transfers" download area (top pane) they will usually be red and winmx will follow the default settings to search for files every now and again, read along any selected file line to see the current setting, you can change the settings for each file to look at faster intervals using the controls above the list-view.
If No "incompleted" files are shown in the download area but you have some entries in your "incoming files" location then return to the "Transfers" window and click the button that says "Load Incomplete" and that will scan the incoming folder and add the missing entries.
Once the entries are visible you can right click on them for further options such as search for alternatives or search for further sources, be aware that alternatives might not match up to the file you have a partial of so find further sources is the preffered option and is simply done by winmx internally matching the files hash with those it finds on the network to ensure its the right file.