Ask away .. Advanced Search will give you more parameters to search with.

Advanced Tools menu:
For LW Pro you will most likely see 5 ultrapeers you are connected to (LW Basic only 3.) Unless you are yourself running as an ultrapeer then you will see more.

When not running as an ultrapeer your node is referred to as a Leaf (most people run in Leaf mode.)

If you have a firewall issue it will show this on the left side of advanced tools window.

Incoming searches are those that in some small way link with files you are sharing. This might not be a good match of your shared files though you may notice. This information is not highly important however.