Showing Category Items + Sub Category Filter

1. Is there a way I can to call for displaying a specific category of items on one page?

I currently use category URL:
But this method doesn't allow me to have sub filters to choose from, or the option to have a side bar.

2. Is there a way to insert a custom blog category filter on a page?
For example: I have a category called fruits. I want to have a page showing my Fruits Category. On this Fruits Category page, I also need the option/filter to browse sub-category such as Apples | Oranges | Watermelon | Grapes.

Please advice?