Is there a way to get a file or a tab editable by the user himself AND by a connection ore connection type?
No; not without the fieldtype being designed for it. As far as I am aware none of the fields are except points and rating fieldtypes.
The possibility to write on the cb-wall should be restricted to the user himself AND one of his connections (or a connection type).
You could use CB ProfileBook then use CB Privacy to let the user restrict the tab to himself and connections only, but this would also affect display of the tab unfortunately.