1-LW is installed in my Applications folder
(running any app from a DMG is not recommended). [edit: same results with the InstallAnywhere installer on the G4; completely removing all traces of LW makes no difference either]
2-Right
3-just checked: not a required step.
4-Right.
5-The beach ball freeze won't allow either the about or prefs window to be closed, hidden,minimized or cancelled by either the mouse or the keyboard but the LW window and the topmost window can be dragged to different positions. Parts of the gui are still working--e.g., results in the Connections columns like time, messages, etc are changing, but I cannot switch panes or use any LW menu items, so have to force quit.
Console doesn't log any activity but Process viewer shows LW working actively.

I can't trigger the freeze using the Advanced stats window, nor by highlighting text and clicking oin the dock.

Clicking on other dock icons doesn't freeze the prefs or about window--looks like clicking only the LW dock icon is required.

It's sure good of you spending your evening on this--wish I could help more efficiently.