No, you don’t have to have a canon specific cable. As long as the USB cable has the right "ends" it will work. You do not have to have the CD. When you plug the camera in, it should find the software/drivers so that it will move the pictures.

You can use your Photo shop elements to manipulate and load the pictures. But you can also do it through your explore screen.

Another option you might consider is just putting the compact flash card into a card reader and load them that way.
References :
Sell cameras for a living, also personal experience. (I love my XTi!)

I personally use a card reader and the explore function then do any editing in my software of choice for what I am doing with that picture.

If your shooting in the RAW format then you will either need to use the software provided with the camera (RAW converter) or you will need to use the Adobe Camera Raw (ACR) plugin with Photoshop. If your shooting in jpeg format then any imaging software will open the file.

As for the cable, anything will do as long as the plug to the camera is the right size. Also, if you have a card reader it can be much faster removing the card and plugging it into a card reader.
References :
Pro Photographer