I'm not sure I understand your problem...

The # column on a search only shows the number of hosts that have the file. The 'Name' column usually shows the file name - do you not have a name column? - You could right-click on the column headings in the search results - this will give you a drop down list of headings you can select.

LimeWire does not normally disconnect from the network - the problem is probably somewhere else. Depending on how you connect, your provider may disconnect you periodically, or you may experience occasional line noise that interrupts your connection. If your computer is overloaded (processor) then there may be insufficient time devoted to handling communications to maintain it.

The network changes as people join and leave and clients find new ultrapeers. The network is particularly fluid at the moment - so your local group of clients tends to change quite rapidly.

Each client decides how to interpret a search - LimeWire clients will respond differntly to a search then morpheus clients (bearshare, shareaza, gnucleus, etc.).

Mark