Solution:

What

It stated 'WHAT' was the father's name.

Solution:

5625

n^1
75 * 75 = 5625 (sum of first 75 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).

Solution:

The mathematician made a small fence around himself and declared himself to be on the outside.

Solution:

Velma waits until night time and then goes through the second door.

(No sun at night)

Solution:

Mark Benson '?' = question MARK, so the note on the door reads 'Question Mark Crimson broke your window.'

Solution:

If you zoom in, you'll actually notice that the building on the left is closer. The highly perceptive person who noticed the satellite dish was right all along!

Solution:

0.5

Explanation:
Rachel Age = 10.5
Diana Age = 0.5
10.5 + 0.5 = 11

Many must have guessed the answer as 1.

Solution:

It is a mango tree.

Solution:

He was watching an emotional movie where an old lady died.

Solution:

The original password for Jasmine's account was 'changed' and the new password is 'distinct'.