Why is it sometimes when I type in a popular group,say G** Wh**e 4 times
I get the same number of "hits" with the same number of songs- 0?

What you need to do is instead right-click the search tab & choose Find More Results.

Various reasons if you might not be getting any results. Each person only has a limited search horizon. A single search will not search the entire network. If it did, a single search might take 1-2 hours to finish (with the side effect of slowing down the entire network if everyone did this.)

So searches can depend on the people your ultrapeers are connected to. And then, sometimes some ultrapeers do not behave properly returning results when they should.