No. Each cookie stores information about 1 specific site. Since his problem is occuring with different sites it can't be cookie-related.
No, a virus would not change your window size preference, it would do much more damage. But it's definitely a good idea to use spyware and/or adware software if you are running windows.
Exactly, it's just a preference.
Try this:
Make Internet Explorer Open in the Window Size You Want
Periodically, Internet Explorer (IE) forgets the settings for its window size and decides to open in an annoying small window. If you close all other IE windows that might be open, resize the small window (do not maximize) and then close it, IE is supposed to remember that it was resized when you next open it. But sometimes it goes right ahead and opens in a small window again. In that case, there are several methods to try.
Resize (with only one window open) and then close by clicking the X in the upper right corner while holding down the Shift key. Often this works but it may not.
If the above does not work, your next step is to try the two-window method.Open a single IE window (which is presumably still too small)
Now open a secondary IE window by either right-clicking or shift-clicking on any convenient link in the open IE window
Resize this second window to the desired dimensions
Close this resized window by clicking the X in the upper right corner while holding down the Shift key
Resize the still open original window as desired
Close this window by clicking the X in the upper right corner while holding down the Shift key
If you do not mind always having maximized IE windows, another approach is to edit the IE shortcut. Right-click on the shortcut that you use for IE and choose properties in the context menu. In the drop-down menu for "Run" select "Maximized". (Secondary IE windows will not inherit this setting).
If you are fed up with IE I highly recommend installing FIREFOX (free).