When the thumbnail and image sizes are specified, does the component physically resize the images, or is this done in the browser? If they are resized, do they replace the original folder images, or are there resized versions placed somewhere else?
a) Pictures are resized physically. Browser resizing will make loading page too heavy.
b) Resized copies of the pictures are placed in QuickGallery folder under the portal root.
Does the enterprise version of the module allow unlimited module installations on multiple dnn portals even if the portals have different dotnetnuke installations?
Yes, it does.
Is there a way to add a description and or an alt tag to the images? Can you edit the appearance and layout of the thumbnails through CSS?
Quick Gallery is made for quick and easy pictures gallery building. Therefore, the only way you can add description to the thumbnail is by naming your particular file as your description. Say, you will need to name your file as red_flower_in_Joe_garden.jpg that way your description will be "red flower in Joe garden". Same for the alt tag. In case you need more control over description of the image you might want to check Coding Staff Portfolio module.
Quick Gallery view layer is based on pure css, no tables or deprecated elements. Therefore, you can modify module.css file the way you want it to be modified.
I can't see the folder and files in it I've uploaded using FTP.
You need to make sure you can see this folder using Admin->File Manager. If you don't see the folder in File Manager, then you need to synchronize your folders using "synchronize" button on top of your folders list in dnn File Manager.
What is the JavaScript library that the module uses?
Module uses JQuery javascript library + pretty photo jquery javascript plugin.
How can I format the Gallery Page layout?
You can use CSS and create a specific container for the module. If it's not enough for you, you can change anything in ascx file (layout, structure, etc.)