Yes, it can. Just admin should enter in his admin area -> FAQs list -> then click to edit the question. Then select the new category and hit "Update FAQ" button. That's - simple.

Yes, you need a web server  to install the scripts:
1. Upload the script via ftp to a directory on your webserver;
2. Create a MySQL database on the server;
3. Run the installation wizard of the script and install it on the webserver

All the scripts made by ProfiAnts(Simple PHP Scripts) required PHP 5.2 or higher and MySQL 5.0 or higher to run on your web server.