It's shouldn't noticably affect it. You can adjust your upload bandwidth by going to Tools>Options>Uploads>Basic, adjust it down 5-10 KB/s from your max.
In Limewire go to Tools>Options>System Tray, and put a tick beside "Minimize to System Tray", click apply.
If that fails, try deleting your pref. folder(with LW completely shut down), point 3 in this thread:
Fixes for Limewire when LW isn't operating as it should! Make a note of your settings first cause they'll be reset to the defaults.