In the CGI::Application framework is all the functions such as: setup(), cgiapp_init(), teardown() etc. executed every time the application is run? Or is there anywhere I can init stuff just once?

See CGI::Application::Loop.

is there any way I can pass in parameters to the called function? for example a static page argument on which page to print to the printStaticPage function?

CGI::Application does have a param method ...