「質問の意図がわからず、間があることが多かったので」の意味
英語でこの文は何でしょうか？
私が思ったのは
Without understanding the question's meaning, there were lots of spaces.? か
Because there were lots of black spaces one cannot understand the meaning of the question.

Question

Answer

I think it means;
It often happened that they couldn't answer quickly because they didn't understand the question's intention/purpose.

間がある= there is an interval = it takes a while to do something

In this context, it takes a while for them to react the question.