Organising iTunes and folders on computer

I have a frustrating problem.

Let's use The Bangles as an example. I have several of their songs in my iTunes library. Some of them are on compilation albums and some are just singles. When I search for them under Artist, it doesn't show all their songs.

I have a huge library and often wonder if I have a particular song in there. Sometimes if I don't see it under the Artist, I might buy it again, and then find out that I did actually have it before, but it didn't show up for some reason and now I have two songs the same, not to mention unnecessary spending.

It also seems that the iTunes library is a different layout on the computer than the phone, so I can see all the songs for a particular artist on the computer, but not necessarily on the phone.

Then there is that thing where the message comes up saying that a song can't be located, so I have to go and find it again. Why does this happen when I don't remember moving it?

I also have a different dilemma of how to organise the music on the computer as I like all the artists to be in the same folder, but if I have compilation albums, I also want to be able to keep all the artists on that album together too. I suppose I could put the specific song in both the artist and the compilation album folders, but that would mean having a duplicate wouldn't it?