First, you should really send this sort of issue to the support e-mail address; the forums are meant to be more of a community resource than a means of direct support.
You don’t say how you are trying to exit the browser: Keyboard commands? Menus? Clicking the close button?
Again, how are you trying to launch the browser?
Where are you typing the URL? It sounds like the browser has not been launched when you enter the URL. How is the history “interfering”?
Which browser are you launching? What does Spotlight have to do with launching the browser? Spotlight is the Finder search utility.
We’ll be happy to try to help you resolve these issues once we have a better understanding of what you are doing.