I tested it with two different external applications. The first one being the infamous cmd.exe window, the second one the rxvt terminal.
Either of them qualifies as GUI application. I think you should test text editors like notepad, word, word perfect, open office, vim/win, xemacs/win etc. Anyway, in my opinion, selection clipboard separation is a must and lyx/win should not middle-button-paste from external applications under windows, nor from system or internal clipboard.
3) In LyX, select something then click somewhere away and press the middle mouse button. The selection goes away
This is what I have discussed. Some word processors keep selection and some do not. Lyx currently only paste from active selection so left-button click will clear selection.
and what you paste is what already was in the clipboard, not what you selected in LyX.
This is totally wrong. Middle-button-paste should not paste clipboard.
4) In LyX, select something and then press C-c. Now click somewhere else and press middle mouse button. What you copied with C-c is pasted.
This is wrong. see above. Actually, such topics have been discussed many times and we had never reached a consensus on the correct behaviors. Bo