OS Winxp Pro
Limewire Pro

Question 1) under "Library" and under Hits I note the number of "hits". I don't understand how you can hit without a download. Are these fellow file sharers that have highlighted the description but not clicked to download?

2) Under "connections" I note that I always have 5 outgoing Hosts. I am not sure what this means. I can't add to or subtract that number of 5 hosts.

Thanks for any suggestions.

Q. 1)
Well I'll take a shot at this. From my understanding the hits are the representation of how may times a search has been done for that file, and it has returned your file in the search results that number of times.

Q. 2)

What you are seeing is the number of Ultrapeers connected. In LW basic the number of connections are 3 in LW Pro the number of connection are 5. Those numbers are pre-set in the program.
From my limited undertanding of how the program operates the only time these numbers might change, is if you had a connection speed that might support you as an Ultrapeer, then you would see peers and leaves.

These connections are a good thing for the G network

It appears from your description you are connected as a Leaf shielded by 5 Ultrapeers and you are using LW Pro

On the LimeWire support page there is a guide you can download and read. This guide has lots of useful information.