Whenever I clicked on Category it doesn't show subcategory, instead it tried to show listings on that category which is not supposed to be so.
Secondly, how do I make the categories on mobile a slideshow

@Theboss
Based on your screenshot you have categories on mobile.

Yeah, that's categories on mobile. If I click on it it will take me directly to listing page instead of subcategory page. How do I change the action to subcategory page imstead of direct listing page.

How do I extend the header picture to the mobile category region? I don't like the white background of the mobile category

@Theboss
Subcategories menu is not available on mobile. For customization consider looking for developer, people are not open to do someone else job 

Try the Veronika theme and see what I'm talking about.
Try other themes as well. This is not about doing someone else's job, this is about doing the right thing. That's the way it should be. Category>Subcategory>Listing. Not Category>Listing

@Theboss
Reporting personal preference as bug will not be accepted.
If you think something else is correct - you are ready to go - we deliver all theme files.