1TB means 1024GB. That is more than most people will ever need for anything. An operating system like Windows 7 only takes up less than 20GB.
Maybe, depending on the enclosure... BUT, it's not worth it when you can just get an entire new external hard drive for barely more than the price of just buying a bare hard drive. Here is a brand new 1TB external drive for a laptop for $60: http://www.newegg.com/Product/Product.aspx?Item=N82E16822236576
You can load most OSs onto any hard drive, as long as you select to boot to it while your computer is turning on. However, USB drives are much slower than internal hard drives, so it will be very laggy.
What you could probably do is just replace the internal hard drive on your computer. Most laptops have a trapdoor on the underside with a couple screws to pop the panel off and then take the drive out and replace it. You just need to make sure the replacement is the right size and is compatible with the specs of your computer. For a desktop, a hard drive just pops in to replace another one, or you could have multiple internal hard drives.