About header images for each category article

To Whom It Mat Concern,

I’m sending this message since I think I have some problems and I need your help.
Here’s my demo website. (not published yet)
https://svpro.jp/blog/cms2/

On this website, I would like each category to have its own header image and its own site logo (the icon image at the top left of the banner).

On the demo site, I have created categories “ROCK”, “BLUES”, and “JAZZ”.
As you can see, when you click on ROCK, BLUES, or JAZZ in the top menu (the menu at the top of the page), it changes to the header and the image prepared for each category.

I was able to get this far with the settings in the theme admin panel, but I have 2 problems.

1) First of all, when I display an article set in the ROCK category, the site icon and header image are for TOP. I would like articles in the ROCK category to display the ROCK site icon and header.

2) The next, when I click on the “ROCK”, “BLUES”, or “JAZZ” site icon, it also takes me back to the site icon and header for the TOP page. Instead, if I click on the site icon for each category, I want to go back to the top of that category (archive).

Could you tell me how to fix them?

Thank you very much.
Sincerely,