1. A search is not continuous. It searches a % of the network. Searching the entire network would take over an hour per search. So in most cases it will search local areas & any overseas peers you or others you searched may be connected to. To reactivate a search there's a few options. 1. you can type the 1st 1-3 letters of the search in the search box & it will fill out itself. Then press search button. Another option is right-click the search result tab. You'll see options here. In one is the option to repeat search & another is to 'Get More Results' which can be very handy.

2. All search history is forgotten when you close LW.

3. Yes all continues. I believe one UltraPeer you're connected to drops off to make it available for others to help them connect to the network. This should have no effect on your LW's u/d activities. You don't need that UP because whilst in idle mode you're not searching the network.