problem no. 1: the two of you have different problems.
first guy - are you behind a firewall, router, proxy server? are you connecting from home, school work? what type of modem are you using? have you run the telnet test, to see if you can access the Gnutella network?
http://www.limewire.com/index.jsp/faqs#sta3
second guy - your downloads are saved in your Shared folder (go to LimeWire options and click Sharing in the left column). use a third-party music player to play music files, like iTunes or QuickTime, and remember that LimeWire is not a music-management application. once you download the files, play them in iTunes or QuickTime, just as you would any other music files.
zbell