Creating A Sidebar Left Video Archive Page like example

Hi team,

i am trying to create a new archive page like this:

https://www.quicksprout.com/university/

1. I've managed to get the sidebar to display left on this archive page, but a few questions remain.

2. How do I get the sidebar to display Categories showing specific posts from that Category only, but with the different mini categories?

https://drive.google.com/file/d/1RSe814GGaYyNFcFpqjFnGVuI55FCoL-B/view?usp=sharing

3. How do I add a search bar at the top of this Archive page, that searches for posts from this archive? I understand from another post that I have to use a Before Content Hook to display the widget, but all i got was the generic search widget that WP provides, which is not what I'm looking for.

https://drive.google.com/file/d/1ddQ7Ot8Lx4cKlD0JERGtXmtlrvastj0t/view?usp=sharing

4. Lastly, how do I get the posts to display in this way instead of the one that GP provides right out of the box?

https://drive.google.com/file/d/1WKdGaZtnTp4I8tFaswfLJ89B_xC6Mp0s/view?usp=sharing

Thank you so much!