I can't find any K2 search module; I googled a bit and it looks like K2 has no integrated search.
I only found commercial plugins for advanced search, but I need something free.

Does K2 offer a search module that searches in extrafield, allows to select categories and fields to search into and so on?

If not, I would probably neeed to change component, because it's definitely necessary for the project I am working at. Do you know any good alternative?

I'm afraid I don't know of a free solution for something like this.

Thank you.
It looks like Flexicontent has integrated advanced search, so I am trying that component... I write it here in case it is useful for someone else who has my same problem.
I hope that someday K2 will offer this free feature too.

We will see in the upcoming K2 version ;)