I know there have been issues with fetch, I am not sure about godady. I use IE on my PC and FireFTP on my mac.

Yes you have to copy everything in the folder including the sub folders images and thumbs, to your server. First test that the gallery works on your computer by double clicking the index.html on your c: drive. This will run the gallery locally and ensure you have everything working before moving to the www

You can put it into a sub folder on your web server though if you want to.
For example on my web server I have the root folder for my domain phillipnorman.com
Under that I have several folders to organise my stuff, one is called 'weddings' and one is called 'cathandcaleb'. In each of these folders I have all the simpleviewer files for each gallery including their own individual index.html, images and thumbs etc. So each gallery can be accessed by www.phillipnorman.com/weddings/ and www.phillipnorman.com/cathandcaleb/

How you link to these two folders (and therefore the galleries in them) is entirely up to you and can be done in many different ways. regardless of how you address these folders the structure and files in each remanes the same.
The simplest way would be to have your main page index.html in your root folder (phillipnorman.com in my case) and have a simple menu that opens each gallery in the same or a new window using a standard href link like:

<a href="/cathandcaleb/" title="Cath & Caleb">Cath & Caleb</a>

Hope that helps...