One Shopify store can have multiple domains and you can force all other domains to redirect to a main one, if that is what you want.
Check out this post from last summer: https://ecommerce.shopify.com/c/shopify-discussion/t/multiple-domains-for-one-shopify-hosted-account...
It gets into some of the SEO questions you have.
at the moment, the extention I want to use primary has no "content". I'm not that familiar with domains, but will this change in adding this domain and make it primary do all the 301-redirects automatically?
Lets say I have a blog-post "paleotogo.at/blogs/main-dishes/21097501-fried-rice".
Will it automatically redirect to "paleotogo.org/blogs/main-dishes/21097501-fried-rice"?
Thanks in advance for your help.
Yes this should work fine.
Let us know if you run into any issues.
I assume you are trying to do this: https://support.google.com/webmasters/answer/83106?hl=en
You probably need to verfiy rhat you have permission for the other property first and that it is accoicated with your Google account.