very well, i assume that pretty much says it all.
Given that Filemaker can use ODBC to function as the front end of another database such as Oracle, or SQL server, it sounds possible. Given that I have never worked with MySQL, I can't tell you for sure.
are there are pre-designed query sheets that can be used to yank the
information needed from the mysql database and display it directly on the website?
This has nothing to do with Filemaker. The visitors to your site need to interact with the database directly (most likely through PHP). It would be different if your site were hosted entirely by Filemaker Server.
IMHO, using Filemaker merely to administer an external SQL database is not an optimal choice.