In Easychart you have to select "Save Graphic File." This option under the file menu will allow you to save a graphic that you can manipulate in a graphics program and then include on your web page.
For larger projects I suggest you use the "Internet family tree" option to design a website of your tree. (But you will have to have server space and be careful of what information you post for public viewing.)
Both of these options might take a bit of practice to perfect, especially if you're using frontpage and expect automatic results. Good Luck.
Sorry I can't help on the printing problems, other than to say that I don't have any problems on my brother laser or epson inkjet.