RE: When the search window opens, (using the "Advanced" Tab) the "Account" Filter is populated already. In this case, it displays a checking account.

I've tried but have been unable to duplicate this. Are you sure the window wasn't already open? It can be hard to tell if you have a lot of windows open or have the View | One Window option set, though in those cases you should be able to see it on the Window menu, which lists the open windows.

RE: Therefore, I can't search for anything that does not include that account... I have been unable to find a way to open the "Find" window and have no filters present.

You can delete any filter by clicking on it in the "Current Choices" table and then press Delete on your keyboard.