Is it possible to add content from a external api to Contentful headless-cms? Let's say I create a content type "product-feed" which enables the author to filter products from our shop backend. Therefore it should be possible to retrieve categories, brands, etc from our shop api.
Yes, it is possible. You'd have to build your own custom ui-extension. It is a small html + javascript app that you upload to Contentful that would talk to your backend api and display your products etc. in the Contentful UI.
You can see several examples and code here: https://www.contentful.com/developers/docs/extensibility/ui-extensions/