Can I copy software from one computer to the next?

No you need to download it directly into the pc

If you have the image or the complete install, surely. If the program is already installed you can copy the program folder but it will need the 100 to 2000 registry entries that go along with it and that will be practically impossible to isolate all the correct ones needed for proper operation.

Yes , if the terms allow you to do so. You also need the installation media or file. Simply copying the directory folder, wil. Miss some files or the registry entries and will fail.

Not possible. Only thing you can do is exchange the hard drive.