I want to use search and filter on standard archive for category page /category/{category_name}

The category has published posts. Filter contains tags, search and date. I am using ajax loading and auto submit form. WordPress is 4.1

I tried two methods:

shortcode –
when I open a page with filtering I get No Results Found message
when I change filter form I can also see – No Results Found

archive page –
when I open a page I get all results (good)
when I change a filter form for tags and date I get first two posts – they are wrongly filtered
when I change a filter form for search i can see message “nothing found”
when I uncheck all tags delete search and date texts page displays first two posts.

I think the two methods are not working because of the same cause. What can be wrong? I can provide more info if necessary