It seems that I should save all the website content and scripts in a MHT file with IE, then run the MHT file.
e.g. for the http://www.weewelcome.ca/weeapp/index?N=0&Ne=1 website, if I save all the website content and scripts in a Webpage complete HTML file, then the five images will stop rotating offline.
You can avoid most problems, aside from absolute urls, by running a server on the local machine and storing and serving 'offline' content from there.
The best way to prevent any potential conflicts you may have with viewing your scripts would be to run through a local server.
I would recommend XAMPP
Once you are done with the setup, go to your C drive -> XAMPP and store all your files within the htdocs directory.
To run it, you type:
http:// localhost/your_filename in your web browser.