I'm planning on installing wordpress on my site and I was wondering if there are any other free programs out there to do what I need (such as Calendar, Polls, Counters, etc.) that I can embed/build on my own site (like wordpress). Or, if none of these are available if there is some web guide, tutorial or template to build such things.

You can browse for Wordpress plugins http://wordpress.org/extend/plugins/
Just search for plugin you need such as calendar, download it and upload to your server. Then you need to activate it in your admin area.