Yes, Fantastico is what a lot of people use to install & upgrade Wordpress (although I advise doing thorough research first before upgrading to a newer version to be sure that all your plugins and Theme files will be compatible, to save yourself a headache)...so that is a good way to go.
On editing your pages and posts the answer is yes, you do need to be connected to the web to add content, but you can use a program called Windows Live Writer (free) if you're a Windows user to create your content offline, then it "published" to your wordpress installation for you when you are online and you tell it to. I don't use it since I am a Mac user, but a ton of people do use it and like it (for Macs I like Mars Edit even though it's not free).
When you're transferring everything to the new site, you can either copy & paste the plain text into WP, then "style" things in the visual editor where you see the buttons for things like bold, italics, colors, etc. OR you can copy the HTML from your DW file into the HTML editor (just the content section, not the whole file) but be careful about any style declarations you've made in the HTML (such as id=" or class=") to be sure those id/classes are in your Theme's stylesheet.
There is no "uploading" like you do with DW - you just "publish" the page or post when you're satisfied with it, and even when it's published you can go back and edit if necessary, but be cautious of too many edits on posts - WP will "ping" google whenever you publish or edit a post, and they don't like too many pings on the same post - it gets annoying to them.
If you want (or need) to modify your Theme's files to customize them (which I only recommend to those that are very adept at HTML and familiar with PHP) you can do that on your laptop (keeping a backup copy of the files of course) and then upload them to your theme's folder to overwrite and modify the original theme files.
A great place to learn more about WordPress is at http://wordpress.tv/ - click on the link at the top that says "How To" and browse through their video tutorials.