If I take my external drive and put it inside my computer as a second drive, if it already has stuff on it, like music, files, ect.. will it keep them intact or format it automatically?
It depends what software you have running on your computer. If you're just running an operating system, then no, I don't know of any common operating system that will automagically format your hard drive when you start up your computer.
That being said, if you did happen to have Darik's Boot & Nuke (DBAN) on a USB flash drive that you booted from, or it was installed on a hard drive, than indeed everything would be gone. The point is, you should know if the drive will be erased or not, because it depends what you have on the computer. Obviously the DBAN case is less likely to happen, but it's not unheard of to see viruses corrupting/infecting files on external drives, or ones whose payload is simply to format all the drives in your computer.