Hi @Bettina_Lucas, thanks a lot for the post, sorry for the delay. Regarding the changing of the doctype, At the moment, it is not yet possible to do this in Webflow, so this is something that would have to be done after export.
On the errors/warnings on the W3C checker, I did a check on the Webflow site: architekt-conen.webflow.io
The W3C checker at https://validator.w3.org/nu/?doc=http%3A%2F%2Farchitekt-conen.webflow.io%2F reported 3 errors and 15 warnings.
Although it should not happen, somehow there was two elements on the site with the same ID. I would suggest to change one of those IDs referenced in the html by line number. You can view the page source and search for "id="kontakt" to find the instances and then change it in the designer (or on the exported page) and republish.
Error: Attribute wait not allowed on element input at this point:
This looks to be due to the Wait being used for backward compatibility with older browsers.
Element style not allowed as child of element body in this context:
This looks to be caused because there is some custom style used in the Footer of the site:
My suggestion would be to put that in the Head of the site, instead of the Footer.
As you indicated, there seems to be more validation issues on the exported site, with the ones that are different from the Webflow site, mainly being syntax related issues. I would check the edits that were made to the html after export on those.
I hope this helps!