When you create an HTML file with images and links in it, you're basically telling it where to look to find the picture or whatever you're linking to. The best way to do this is to have everything in one folder... the html file, as well as everything it links to. I'm assuming that what you're doing is creating the page and then moving only the notepad html file to your other computer. When you do this, the image tags in the notepad file look where you tell them to, but they're obviously unable to find the file. You need to move the entire folder if you want everything to show up correctly.
As for copying a website into notepad, its basically the same idea. The code looks for the images and such, but can't find them. They're stored on the company's server and not on your computer.
So the basic moral of the story is that you need more than just the html file in order for a page to display "properly". You need to have all the files that go along with it as well.
