Hello, please find my feedback to your comments below.
1. Display only parent taxonomy items from 'temaer' in search.
Usually when you use the "Add filter" button to insert a taxonomy search filter in a View, the system will automatically include a shortcode like this:
[wpv-control-post-taxonomy taxonomy="book-tax" type="checkboxes" url_param="wpv-book-tax"]
By default, all terms will be displayed as options in the filter and there is no simple, automated way to specify "only parent" terms, or "only top-level" terms, or "only child" terms, etc. That filtering option does not exist in Views, but there is a different shortcode available for a more customized filter control - wpv-control:
https://toolset.com/documentation/programmer-reference/views/views-shortcodes/#vf-153286
You can use this syntax instead of the wpv-control-post-taxonomy shortcode to create a similar taxonomy term checkboxes filter with predefined options:
[wpv-control url_param="wpv-book-tax" type="checkboxes" values="parent-term-1,parent-term-2,parent-term-3" display_values="Parent Term 1,Parent Term 2,Parent Term 3"]
As you can see, the terms and their corresponding slugs must be defined manually in this workaround. The terms must be listed in the display_values attribute, and the corresponding slugs must be listed in the values attribute.
2. Display only parent taxonomy items from 'temaer' in other contexts
The wpv-post-taxonomy shortcode does not provide any options like this to display only parent terms or only child terms. If you are using this shortcode to display terms in some contexts, you will most likely need another solution. A View of terms filtered by term parent = "None" might be a good solution instead of the wpv-post-taxonomy shortcode.
https://toolset.com/documentation/programmer-reference/views/views-shortcodes/#wpv-post-taxonomy
3. In all these different contexts, have child "temaer" link to their parent (e,g. in blog, events, retreats, podcasts, videos and other posts).
Again, the wpv-post-taxonomy shortcode is not flexible enough to provide this feature, so a View of terms is probably required instead of the wpv-post-taxonomy shortcode.
In a View of terms, you can display a link to the current term archive using the wpv-taxonomy-link shortcode: https://toolset.com/documentation/programmer-reference/views/views-shortcodes/#vf-153464
Displaying parent term archive links instead of child term archive links will be a bit more complex, and you may need a custom shortcode solution.
I'm writing this last part, because optimally all the child theme would link the the post of the parent theme. But maybe this can be done by using the child slug in the links. What do you think?
I do not understand how you hope to use the child term slug in links, but redirect to the post of the parent term. How would that work? Can you show me an example?
Am I doing this all wrong?
I think this is a difficult question to answer. It is somewhat subjective. In my opinion, redirecting to a parent archive when clicking a child term link is confusing. I would not expect that behavior, but maybe it is not as noticeable to your site visitors, or maybe they would not find it confusing, it is hard to say. It could also have significant impact on SEO. Removing child terms from a custom search filter can make it difficult to find some posts that have no parent terms assigned.