Header ad only for desktop

Hello,

depending on your theme you can use automatic insertion at one of the available positions:
https://adinserter.pro/documentation/automatic-insertion

Alternatively, you can insert it before or after HTML element:
https://adinserter.pro/documentation/automatic-insertion#before-after-html-element

This works regardless of your theme.
If you can be more specific on where you would like to insert it, I can suggest settings.

You can use device detection to limit insertion to desktop devices:
https://adinserter.pro/documentation/device-detection

Insert After HTML element .site-branding

Correct.
But don’t forget to enable all the wanted page types:
https://adinserter.pro/documentation/wordpress-page-types

You have a javascript error on the page:

Uncaught TypeError: Cannot read properties of null (reading 'getAttribute')
    at griwpc_tools.GetElementById (base.js:24:10)
    at griwpc_tools.getButton (base.js:62:16)
    at griwpcChangeButton (recaptcha.js:22:22)
    at recaptcha.js:107:17
    at recaptcha.js:107:53

It is caused by this script:
https://bestwisher.info/wp-content/plugins/recaptcha-in-wp-comments-form/js/base.js?ver=9.1.2

You need to fix this error as it prevents further javascript code execution and consequently block insertion.
The easiest way would be to disable responsible plugin recaptcha-in-wp-comments-form.

Which block have you configured for the header?

Now it works fine.
You may need to center it and maybe define a fixed ad size:
https://adinserter.pro/documentation/adsense-ads#code-generator

No.

No, only sometimes a large ad block may be served.

🙂

Thanks for your kind assistance! I really love your plugin and support!

Please say it here:
https://wordpress.org/support/plugin/ad-inserter/reviews/#new-post

Thank you!