Many, many comments here...
First, anything downloaded from the App Store is not capable of making the kinds of changes you describe. Due to the sandboxing restrictions imposed by Apple on App Store apps, they can only access their own files and files that you explicitly give them access to.
Second, you should really never take a Mac to the Geek Squad, as they usually aren't the most knowledgeable when it comes to Macs.
Third, if you still had a copy of Flashback on your Mac recently, you are not installing software updates often enough. Apple released an update that both closed the vulnerabilities Flashback relied on and removed Flashback (if present). It is very important for security reasons that you keep your Mac updated properly, by allowing it to install updates when it alerts you to them. For more information on keeping your Mac secure, see my Mac Malware Guide.
Finally, with regard to the problems on your new machine, did you import anything from the old machine? If so, you may have imported some kind of junk third-party software that did not come from the App Store. See the part about checking third-party software in my Mac Performance Guide... what do those tests show that you have installed?