Wow... you skipped P2P since napster's days? A lot have been happening since. The difference between modern protocols and napster is "swarming" meaning you are dling a file from multiple hosts at a time, so when an host go offline, others can continue your dl and it also speed up the time to retreive files... Be patient, your dl will finish, to help it do another search so other sources might pop up to add sources to the dling file.
Chats as problems, especially if you are firewalled, you might want to open the port 6346 of your firewall or/and router if you have them.
For the files in your shared folder: is it downloads.dat and downloads.bak? They're essential for remembering sources and data of the downloads between lauches of LWire. If it is not the files cited above it sounds like a virus you got. Clean it with an antivirus

Bonne chance