>Is it possible to open notepad and type some gibberish and save it as a .exe file and run it?
If you want to work out the machine code for your system that would be equivalent for a properly assembled executable, then figure out what combination of keyboard characters will give you that machine code...I suppose it might be possible to do this if Notepad doesn't add anything in the process of saving the file as an executable.
Not in Notepad, no. In a hex editor, maybe with a ton of patience. But an exe generally has a header record and sections with headers before them and the like. Try using DUMPBIN on a small exe and see how much crud is in there.
Using a hex editor you could modify an existing exe, but even that would take more patience than its worth.
That's why the compilers were invented, after all!