Ok first things first:
NO SPYWARE WILL RUN ON A MAC.
Right, now that's out of the way, on with the problem.
If you dragged the icon into your trash, it's as good as gone. Select 'emtpy trash' from the Finder's main menu to get rid of it for good.
If you can't find the file, don't worry, it can't hurt you. If you want to find it anyway, open a new finder window, and type 'Orbit explorer' into the little white box at the top right corner. Drag any files it might find into the trash.
As for your surfing difficulties:
mac's can sometimes have trouble with pages not specifically check for use with macs. Try opening safari, go to preferences -> security and activate 'enable plug-ins' and the other check boxes.
also try switching off 'enable pop-up blocking' as that can sometimes cause problems.
If that doesn't work, maybe the page is just offline.
You don't need to worry about using Internet explorer on your mac, it's the WINDOWS version of IE that is vunerable to virus exploits and spyware. The mac version is a horrible program to use, but at least it can't hurt you.
Remember: On mac OSX there are no viruses, spyware progs, adware progs that can hurt you.
You can download these things that are designed to hurt a PC on your mac, but they can't DO anything!
