The firewall icon is bad. If you are running the OSX firewall then you should configure it to allow LimeWire (LW) full access. If you have a modem/router for high speed connection then there's a very high chance it has an internal NAT firewall. You should enable UPnP for it. Else if it doesn't support UPnP then forward a port. These are possible reasons you're getting the firewall icon. See how to here: Connection problems? Check here first! (click on link) which is broken into sections for Software firewalls, UPnP, Port forwarding, & extras.

Another reason LW may be detecting a firewall is where you're connecting from. Such as work or school, they may have their own firewalls. Also your ISP may well be playing a part there. But just check, sometimes the firewall icon shows in icon just after you start the program but disappears after a minute or less, or for some people perhaps a few mins.

For shared files, these can be found in the LW Library window. Click on the folders listed to see the 44 that are being shared. The incomplete folder is not shared per se. But if you have partial file sharing enabled in LW's preferences, then this helps other people downlding the same files & is good for the network.

Normally any changes you make to the sizing of LW will remain next time you open the program. As for windows, go to the menu bar & choose Show/Hide to choose which windows to have open at that time.