<form method="get" action="example.com/?category=1"> <input type="submit"> </form>
action parameter may be any page etc. but it always redirect to homepage. If I change method to
POST - then all fine. What is the problem here?
Your permalink structure appears to be incorrect try changing your code to. Modified, try creating a search form like this and see if you still get the homepage, if so then there will be something wrong with your theme templates.
<form method="get" action="/"> <input type="text" name="s"> <input type="submit"> </form>
Try the following (untested):
action="<?php the_permalink(); ?>"