Hello Elliot,
thanks for your reply.
I worked around the first issue by not picking a custom slug but using the normal one that is generated from the options page name. Then I can create custom fields on the options page.
When I do that and save those fields, they do show up in the database, but get_field() returns false.
Thank you for the update, I will try it out and get back on it and let you know if it works.