I am having some problems with our business website that is managed with Contao.
I want to edit some fields of something, that doesn't appear on the regular edit button. To make it clear, this is what I see on the edit page:

And this is what I see are the module details, there is a bunch of stuff that I want to change there, but can't from the actual edit page. Any way to access these options?

If I haven't made myself fully clear, please ask away.
Contao has a detailed role configuration where every field for specific users or roles can be set. If you can't see all of the fields, it's because your user has probably not the rights to edit this fields.
You should ask the person with Contao Administration privileges if he can grant more privileges for your user or user-role.