Does a data inquiry cost me anything?

Not usually. (Article 2 Para. 1 VDSG: "An appropriate contribution to the cost may exceptionally be demanded if:
a. The person making the application has already been supplied with the required information within the twelve months prior to the request and no legitimate interest in a new issue of information can be proven. A legitimate interest exists in particular if the personal information has been modified without notification to the relevant individual;
b. Issue of the information is associated with a particularly large amount of work").