Solution:

Assassination
(Ass ass i nation)

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

Solution:

They use the bricks and dirt from the tunnel to stand on it.

Solution:

Since each one of them gave one answer wrong, this means that each one of them gave two answers right.

Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.

Thus both Student A and Student B must be right with the first question and the answer to the first is two.

If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
Q1. Two
Q2. Three
Q3. Two

Solution:

The woman told him to take out one nut each from the rest of the wheels and use them.

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.

Solution:

4 6 5 3 (from magician perspective)
3 5 6 4 (viewer perspective)

Detail:

From user perspective:
3 5 6 4 => 5 6 4 3 => 6 5 4 3

For magician perspective
3 4 5 6 (ascending order as)

Solution:

Birbal drew another line that was larger than the pre-drawn line. Now the pre drawn line was smaller.

Solution:

Solution is below

Solution:

The two numbers are 4 and 13 whose product is 52 and sum is 17.

Solution:

The attached picture shows you how you can do it. If you were able to deduce any other way, feel free to comment.