You are getting those errors because you are using fancybox v2.x with options for fancybox v1.3.x. The example page you are referring http://fancybox.net/blog is for version 1.3.4
Fancybox v2.x options are new and not compatible with previous versions.
In your case, instead of using
$.fancybox.showActivity(); //v1.3.x
you should use
$.fancybox.showLoading(); //v2.x
.... and instead of
$.fancybox.resize(); //v1.3.x
you should use
$.fancybox.update(); //v2.x