It is possible to open 2 instances of LW at once. But it's highly unrecommended. I've done it by being impatient & clicking the LW shortcut again. But then you might also have 2 copies of LW on your system. Use your OS search engine & search your comp for limewire. If you find 2 then you should remove one. But find out which version it is 1st. Versions before LW 4.4 used the Add/Remove control panel to remove, whereas the later versions you should go to the Start menu >Programs>LW>Uninstall. * Also to kill one of the active ones, open your process manager after Control-Alt-Delete keys held down. *** In fact, this is the best way to find out if you have 2 instances of LW running!!!
As far as unknown files showing up, don't open them. If they are zip files then chances are they are a virus. There's been a spate of viruses attacking LW users recently. Possibly deliberately planted by 'suspect' sources concerned about the music piracy.
To learn more about this see
LimeWire continually Popping up every few seconds & also Opening at System Startup This will also explain the xtra files. Might not be the same scenario but sounds similar.