I would like to know, if there is a web page, where I can find information on types of events in Finnish public libraries (if there is such a classification)?
Yes, there are public libraries in Finland as well. The webpage of the Finnish libraries, http://www.libraries.fi , contains mostly information about Finnish public libraries. See, the Libraries channel, Public libraries, http://www.libraries.fi/page.asp?_item_id=1136 .
On the Front Page and in the section Library branch of this site you can find some information about events in Finnish public libraries. However, the major part of the information about events in public libraries in Finland is published in Finnish and Swedish at the same site (http://www.kirjastot.fi , http://www.biblioteken.fi ).
You can also visit the site of the Finnish Library Association, http://kirjastoseura.kaapeli.fi/etusivu/apua/english .