Hi @rominabuchle,
Thanks for your questions! I’ve added my comments below. 
- I inserted a content offer into the pillar page. The content offer is normally gated on our website and one of the most effective offers we have. Since it’s the purpose of a pillar page, to give the visitors easy access to content, I am not sure what is better. To include the content offer gated or non-gated? Can I only offer it free on the pillar page and otherwise gate it?
Personally I would test this out and see which option is most effective for your business. As the content offer is performing well on its own, you could use this as the main conversion point on your pillar page. Alternatively, if your content offer is a meaty e-book or guide, why not offer up the entire thing ungated as the key content for your pillar page and then include an option to download the pdf version to read later. HubSpot have a great example here - Facebook Marketing: The Ultimate Guide they actually have several different downloads for each section of the pillar page.
From a user perspective, we want to make the information easy to find and easy to digest so having it ungated and accessible would be my go-to.
- The pillar page should be our “Executive Summary” of our business basics and should lead to relevant content. Therefor we entered hyperlinks to our blogs, landing pages and some external sources. For external links I chose to open the page in a new tab. But is this also recommended for internal links? Or should they best be opened in the same window? What is your experience here?
My preference is to always open a link from a blog post in a new tab, that way it’s easy to go back to the original page and continue reading rather than having to hit the back button and losing your place on the page. For website pages, I’d only do this with external links and use my discretion for internal links.
For pillar pages, internal/external links should open in a new tab, but you’ll also want to ensure that you’re using anchor links to break the pages up into sections from a list of contents at the top. This makes it easy for the user to quickly jump to the section they’re most interested in.
What are other people’s thoughts on this? @roisinkirby