Yes, mostly we have American books in our resources.
The Consular Section of the American Embassy: http://poland.usembassy.gov/visas.html
Basic information you can get at American Corner Radom - EducationUSA Advising Centre http://www.educationusa.info/ http://www.fulbright.edu.pl/index.html
We have handbooks for the most popular exams in the USA : TOEFL,GMAT,GRE,SAT. We do not have handbooks for British exams (FCE,CAE,CPE).
Yes, using AC resources and taking part in all events is free of charge.
To be able to borrow books or movies, it is necessary to have a library membership card. During the registration every reader should present the identity card.