How can I check, is my Firefox browser 32 ore 64 bit? It's 3.6.8.
All official release versions of the Windows version of Firefox are 32 bit.
64 bit versions are usually called with a different name because those are not official versions, but third party builds.
For Firefox 3.6 that is usually Namoroka, just like the nightly test builds.
Your user agent shows a regular Finnish Firefox 3.6.8 version
Mozilla/5.0 (Windows; U; Windows NT 6.1; fi; rv:22.214.171.124) Gecko/20100722 Firefox/3.6.8