Solution:

The wife was about to have a baby. They were driving to the hospital. The baby was born, and the wife didn't survive the birth

Solution:

1)The first bit is easy, as the first letter of each plate spells WHODUNNIT IX(A challenge to our Detective.)
2)The second bit is a little trickier, but I gave you the solution.If you read the last three letters in each plate from the bottom up and right to left you get ADVANCE EACH LETTER BY THE NUMBER SHOWN, so advance W by 5 to get B, H by 13 to get U and so on until you spell BUTLER DID IT.

Solution:

445

2=(1+1)1
6=(2+1)2
21=(6+1)3
88=(21+1)4

So 445=(88+1)5

Solution:

Dabid is the killer

drawing room(D) , art room(a) , bed room (b) , ice-cream room (i) , desk room (d)

Solution:

794

The nth term in the series is given by the sum of x^n for x in the range 1 to 3, i.e. 1^n + 2^n + 3^n.

Thus the first term is 1^1 + 2^1 + 3^1 = 1 + 2 + 3 = 6,
the second term is 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14,
and so on.

The sixth term is then 1^6 + 2^6 + 3^6 = 1 + 64 + 729 = 794.

Solution:

BACK

All the others can also be read backwards as proper words.

Solution:

Each word has 3 consecutive letters of the alphabet-
couGHIng (GHI)
thiRSTy (RST)
DEFiant (DEF)

Solution:

SQRT(.2 ^ -2)

Take .2 and raise it to the power of -2 and then take the square root.

Solution:

HighJacking (High+Jack+King)

Solution:

Back To Square one