Factory Reset Questions

First, your problems are almost certainly not caused by any kind of malware. For the performance issues, see my Mac Performance Guide. Also, regarding the malware issue, see my Mac Malware Guide.

Regarding the Facebook issues, it's hard to say without more information, but most likely that hacking did not involve any kind of malware. For example, if you changed the password while on an open wireless network (ie, one with no password), someone may have intercepted the data passing between you and the Facebook servers and made use of it to get access to your account.

Thus, resetting to factory conditions is unnecessary. However, if you do wish to go ahead with it, since you are running Mountain Lion, you simply need to hold command-R at startup to enter recovery mode. From there, use Disk Utility to erase the hard drive, which will destroy any malware if it does happen to be present. (There is no Mac malware that can survive this.) Then quit Disk Utility and proceed with reinstalling the system. You will need to be able to download about 4+ GB from Apple's servers to do the install, so be sure you're on a network capable of doing that in a reasonable amount of time. Next, reinstall all applications from scratch.

I would not recommend restoring anything from your Time Machine backup. Copy any important documents to another drive as a secondary backup, and copy them back to the new, clean system by hand. If you let the system help copy stuff from a backup, it can easily copy too much and end up reinfecting the new system, if the old system was infected with anything and then was backed up.

This is a pretty extreme solution, and is almost certainly unnecessary in your case. But it's not going to hurt anything to do it, either, as long as your data is all backed up properly. Just be sure you have a minimum of two good (and separate) backups, one made with Time Machine and one with something else, before proceeding.

So you are saying that even though this Laptop was originally Snow Leopard, but is now running it on Mountain Lion, that I won't need any Snow Leopard discs?

That's correct. Mountain Lion should have installed a hidden recovery partition that can be used to boot the machine and do things like reinstall the system. Apple is trying very hard to pretend that optical discs don't exist anymore. 🙂

Further, there was a firmware update a while back that I believe should have enabled your machine to boot from Apple's servers (internet recovery mode) if that recovery partition gets damaged somehow. That would work transparently, if regular recovery mode fails, but can be forced by holding down command-option-R at startup.