Hi @tibo,
Thank you for sharing access 
Let’s go through each reported issue.
#1 Header font size
The font size is set to var(--text-xl), which resolves via rem. On the frontend, the root font-size is set to 62.5% by Bricks, so the computed value differs from the block editor.
In the block editor, we cannot override all root styles because they would also affect the editor UI itself. We’ll be providing an improvement but whether this will work on a certain setup depends on how the block editor renders blocks.
Gutenberg has two rendering modes:
- Iframe mode: Blocks are rendered inside an iframe, and Bricks root styles can be safely applied because they only affect block content.
- Non-iframe mode: Root styles affect the entire editor, so we can’t override them.
Your site is currently using the non-iframe rendering mode. The block editor currently only switches to iframe mode when both of these conditions are met:
- All registered blocks use
apiVersion: 3 or higher. If any block is still on apiVersion: 2 or lower, the editor falls back to non-iframe mode. One of your plugins is likely registering legacy blocks.
- There are no classic (non-block) meta boxes below the editor. Any classic meta box disables iframe isolation (not the case in your setup).
This limitation is expected to be removed in WordPress 7.0:
In WordPress 7.0, the post editor is planned to always work as an iframe, regardless of the apiVersion of registered blocks.
→ API Versions – Block Editor Handbook | Developer.WordPress.org
We’ve added iframe root-style handling to our internal to-do list.
#2 Caption styling
The caption and image styles are injected via custom code in your “Single news” template settings. So that styling only applies where the template is rendered, which is why the styling differs from what you see in the block editor. This is expected behavior, not a bug.
#3 Bullet, number, and link colors
Same root cause as #2. These styles are defined on the single Bricks template and only apply where that template is rendered.
#4 Image height not respected
I’ve identified the root cause. The .post-two-pictures-img class is reused in another component, and its CSS is loaded later, overriding the element-level max-width applied to the image. I’ve added this to our bug tracker.