Why are some IP addresses red?

Good question....been wondering that myself!

It means that host is behind a firewall which also most likely means you will not be able to connect to them (outgoing) or download files from them.

No, it means if you are behind a firewall as well, you will not be able to reach this machine unless you have your IP exported.

If you are not behind a firewall, there is a good chance you'll be able to reach the red IPs.

I'm trying to understand the support for IP export. It seems no one here understands it.

What are you talking about? When an IP ADDRESS is RED while you are using LimeWire that means that the host is behind a firewall and it is most likely you will not be able to connect (outgoing) to that host. That host can make outgoing (firewalled host connecting to others) connections but the firewall blocks incoming connections (you trying to connect to that particular host). I'm assuming when you say "IP exported" you're speaking of "FORCING IP ADDRESS" in LimeWire. When you're behind a firewall all outgoing connections go through the firewall which means whoever you're connecting to would think you're the FIREWALL's IP ADDRESS instead of your true one. So when you "FORCE YOUR IP ADDRESS" (a host behind a firewall) it will be able to establish a connection with other hosts b/c now they know who each other are even though the firewalled host can not accept connections. You must also realize that when a firewalled host establishes a connection its b/c of the fact that its outgoing, It can communicate with other hosts.

From LimeWire on my desktop computer, I can see files on my laptop that is connected through a friend's router on a different line to the same ISP. LimeWire on the laptop shows that it is firewalled. LimeWire on the desktop shows some files on the laptop with a black IP address and others with the same IP address, but in red. Please explain.

Red files in your library are files that are not being shared. Black means shared files. You can reverse either of these by right-clicking the listed file & choose one way or the other.