Translation:How many exams do we have this semester?
I think in this example, that would mean more like "per semester" than "in this particular semester".
Actually with usage of "the", it's is pretty specific. With "a", it would be more loosely defined like you state, Jellei.
Why is my English translation of "How many exams do we have in this term" not correct?
"How many exams have we in this semester" is rejected. I think it should be.okay to omit "got". I'd guess you would hear/read the sentence with or without "got" about equally. Not sure if leaving "got" out is totally gramatically correct though.
Well, we did accept such a construction a few times, so I guess we can accept it here as well. Added now.