Which courses are being provided by the university under this initiative?
If you are looking for English courses please take a look at these two sites:
What is the fee structure of programs in English?
There are no special fees for English course. At the University of Göttingen international students pay only a semester fee, which is around 310€ per semester. This semester fee gives you access to all public transportation in the city of Göttingen and the state of Lower Saxony as well as discount at the university´s cafeterias. https://www.uni-goettingen.de/en/40054.html
Is one allowed to pick courses/papers from different programs or does one have to strictly pick one program and then enrol in the courses offered in it that semester?
It is better to enrol in one specific program, sometimes you may take courses from other related programs, but this you have to clarify once in Göttingen or at enrolment time.