First, Dreamweaver is much more than a glorified FTP client! Dreamweaver is a Web site authoring and management application. That is the program you should use to build your HTML, not Fireworks.
Fireworks is a Web layout/design and graphics production application. Fireworks can export HTML or HTML and CSS, but that export ability is intended to create mockups and prototypes, not live sites. The code Fireworks creates is...well...awful. You need to learn how to write HTML from scratch, not let a graphics program write it for you.
The single .png file is also not going to work for you. The page you link to has several separate images. You need to create slices on your Fireworks document and export them as individual images, which you then reference in the HTML.
Here are a couple of good tutorials for beginners:
This tutorial is on the general theory of slicing. As such, it's helpful: http://www.slicingguide.com/
In Fireworks, you use the slicing tool (looks like a green rectangle), to draw slices over the areas you want to export as individual images. These green rectangles appear in the Web layer. You can set the export properties of each slice separately. When you export, you can export all your images, or just the images from selected slices. And I really haven't said anything, so start with the help files, then post back with specific qustions.
As to your 403 error problem, it's something with the configuration of the server, it has nothing to do with Fireworks or Dreamweaver. Read these articles:
Also...there are .png files and .png files. Fireworks takes the basic .png format and expands it to contain the vector and layer data. Other applications are not capable of interpreting the special Fireworks data, and will only show the visual data as flattened, even though it's all still in there. Consequently, when you want to produce a .png file for the Web you want to export. Exporting produces a flattened version that has much less data in it (and so is smaller).
Some time ago, I read a tip on this forum that I try to follow. Name your working Fireworks documents with .fw.png and your flattened, exported images with .png. That way, it's easier to keep track of what's what. It's also a good idea because Fireworks will happily write a flattened image over a working document of the same name, causing you to lose all the detailed work you had.
In the File menu, you Save your working Fireworks document, but you Export (or Image Preview, then Export) flattened images for the Web. Save your work, export for the Web.