I don't know what the technical term for them is, but - say you open a program and it opens as a smaller window on the screen. Is it possible to 'set' those windows so that they will open in the same place and at the same size every time?

In general they should do so. Or reopen where they were closed.

As to Windows windows there are options when you right click the Task Bar to Cascade or Tile etc.

If you mean windows in your IE browser do the following.

Open a window and drag the coners to make it full size. Next click File and then Exit, when you reopen the window it should open full size.

Another option is to hold CTRL key while File>Exit