I would like to create a further header, similar to the one that is in the general setting where you can put the widgets in, but with more customisation.
I would like to be able to set the colours and put widgets / menus links in it. Is this possible?
In the header area above the feature header, you can configure the area for html (the settings are in the Striking General Panel), and configure it virtually without limitation. As well, you can put in text widgets, which allow for a great deal of code, and to simplify layout, you can use the layout shortcode inside the text widget so you have columns similar to the footer. It also in widget mode accepts all the other striking widgets.
To go any further then that you are going to have to do some php coding in the theme files. If you are not comfortable doing that then you may want to consider hiring someone. In a few weeks we may start offering this type of customization as a paid service, but at this moment our workload does not allow for such.
Users have done sites with everything but the kitchen sink in the Header widget area. It has little to no restrictions.
Perhaps some users who have done some unique header widget areas or at least made some use and customization can step in and contribute to this thread to assist you.