I have no idea how many parts to this there will be. I am going to write one item per post, and yes, they will be persnickety.

Create a new folder (Command-Shift-N) on the Desktop, it will select the name so you can give it a new name. The same holds true for any folder you are in, so long as you are in icon view.

If you are in list view, it selects the name for a split second, then deselects it. This is new behavior as of 10.5. I call it a bug.