Originally Posted by Gonger

It's up to google and if you have structured your website and its navigation properly it should add it under.

Also there should be some meta description and text on these category pages.

But it doesn't always index the category pages. On one of my sites it adds 2 links of posts.

About the search bar, I am not sure, I think you should tag it somehow and again G. to decide when to show it. I have tagged it with a plugin for one of my sites, but it's still not showing.