In VSTS I want to add a field that is available in any type of WIP, like f.e. state is. Is this feasable ? How to do that ?
The idea is to have a SubState field that better defines the actual state of an item.
Yes, you can add a custom field in VSTS. Basically, you add a new Field for one WIT, and then enable it to be shown in a layout for the others. Picklist might be a good idea, if you want predefined list of allowed values.
See detailed howto here. But adding a new field will not automatically have a full workflow support - like updating related fields when the "new" one is changed, for example.
So, - consider customizing board instead of adding a new Field, this is much easier and fits for the most of cases.