I have a Mac-Mini running MAMP Pro. Can it be used for a production web server for serving a MAMP stack web site? Is it secure enough / powerful enough to manage?
a MAMP stack will be as secure as you configure it. As with any similar stack (LAMP, BAMP or WAMP), it will be insecure if you do it wrong.
The question of "Powerful enough" depends entirely on the load that will be placed on it by users. This question can only be definitively answered by running and benchmarking your actual usage. It will vary hugely depending on how the apps being served are written and function.
The Mac Mini is well capable of hosting a low to medium traffic website. The MAMP stack is a problem, though. MAMP is really only meant to be used for development. They configure the security settings in MAMP as to not get in the way of development. Using it in production is asking for problems.
You'd be much better off installing the "real" versions of MySQL, PHP, and Apache. You should be able to do this either using the source tarballs or alternatively through the Macports system.
Sure it CAN be, but the question you really need to have answered is SHOULD you and that will completely depend on what your requirements are.
The answer to security is "however secure your configuration is". The answer to power is a question itself: how big does your site need it to be? You need to do some planning and come up with expectations in order to determine whether or not ANY platform will fit your needs.