Hi,
First I would recommend choosing a theme of your liking, under the Theme Options -> Overall Box Layout panel. Perhaps choosing the ‘Metro white red vertical’ might be close to your needs: https://i.imgur.com/7mDuKPL.png
Then, you can enable the search button under the Theme Options -> Search text button panel.
If you prefer the whole search bar to be white, descreasing the background margin, and increasing the height will do that for you.
You can even change the background color of the magnifier & search button if you want to.
To return categories or other taxonomy terms, you need to chose them under the General Options -> Sources 2 panel. This documentation should give you all the details you need.
I hope this helps!