MySql is part of OS X so I presume it should be able to run on whatever OS .mac is using (you'd expect they're running the latest and greatest), but I am no mac expert - but I found this link
http://developer.apple.com/internet/...rce/osdb.html/
The GD and Imagemagick software are Open Source programs that manage graphics on webservers. GD is mentioned in the mac developer site mentioned above as it is part of PHP (a programming language which is usually part and parcel of an Apache installation).
And Apache is also OS X compatible so I guess it might be running .mac (Apache is the part of the server that produces the actual web pages you see in a browser).
In short, it should be possible using .mac, depends what they're offering you - I tried to have a look but it involves signing-up from a Mac, which I haven't got.
Coppermine is very powerful, easy to install but will take a while to get right in terms of look / feel though there are loads of templates available on the web to transform the default installation.
If you want to have a play around with the admin/user interface look at
http://www.opensourcecms.com/ - the left hand-side menu has a drop-down selection called Image Galleries - that gives you a list of options including Coppermine - when you click on it the right hand-side panel changes to allow you to access demo versions of the program.
hth
Charles