I think you should let your professor know that you need more time to prepare your tutorial. Being given a sheet at 8PM to tutor the next day seems like it would be very stressful.
As for the students not answering your questions... This can be normal. Mathematics students in particular can be reluctant to contribute to class discussions.
Can you give some examples of the kinds of questions you are asking your students?
You might also consider altering your approach. I personally do not think this method is best, but I have known tutors who simply allow their students to do their own work, and assist when a student raises their hand.
What I would often do, although I am not a paragon of tutelage by any means was to begin the class with a worked example on the board - often similar (in method) to a current assignment question, and then allow students to work individually. If I was asked about a particular question several times I would then go through it on the board.
Such approaches can minimise the amount of student interaction which has to take place 'subject to the whole class' as it were, which can sometimes deter timid students from contributing.