If you use Firefox and you drag the download window to any location, it will remember that and will open next time where it was last, so if you or somebody else moved it that would explain it. IE seems to like to open mid-screen regardless of what you do with it, but as I don't normally use it, I can only say this based on one quick trial.
If you have any doubts about the security of your PC, I suggest you follow the instructions here
and then start a NEW
thread and post accordingly. Somebody will be along as soon as to take a look.