Solution:

end up behind bars

Check that the word "END" is spelled in an upward direction behind three occurrences of the word "BAR".

Solution:

T = 1
W = 3
O = 8
H = 9
R = 0
E = 4

For the full multiplication, see the figure.

Solution:

First Person: 3 full bottles, 1 half empty bottle and 3 empty bottles.

Second Person: 3 full bottles, 1 half empty bottle and 3 empty bottles.

Third Person: 1 full bottle, 5 half empty bottles and 1 empty bottle.

Solution:

84

Explanation:
Let us assume that Adam lived for p years.

p/6 + p/12 + p/7 + 5 + p/2 + 4 = x
=> p = 84.

Therefore, Adam lived for 84 years.

Solution:

I am grape.

Solution:

25

Distance between Tribe Q and Tribe S = 40km
=> Distance between Tribe Q and Tribe R + Distance between Tribe R and Tribe S = 40km
=> Distance between Tribe Q and Tribe R + (Distance between Tribe Q and Tribe R - 10) = 40 km
=> 2 * Distance between Tribe Q and Tribe R = 50km
=> Distance between Tribe Q and Tribe R = 25km

Solution:

The missing number is 11.

Explanation:
The patter here is that the number on the right is half of the product of the other two numbers.

(18*4)/2 = 36
(15*6)/2 = 45

In the same manner,
(8*x)/2 = 44
=> x = 11

Solution:

7 minutes hourglass = p
11 minutes hourglass = q

Turn p and q.
P will finish at 7 minutes and then turn it again.
When q finishes (11 minutes), turn p again.
It will take 4 minutes for p to become empty.

The total time if you count is 15 minutes when p empties.

Solution:

It is not Richard because if it was, Richard 1 and Morgan 3 would both be false, which would make Richard 2 and Morgan 2 both true which is a contradiction.

It is not Travis because if it was, Travis 1 and Travis 3 would both be false, which is not possible.

Therefore, the killer must be Morgan.

Solution:

The missing number is 399.

Explanation:
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
258 = 6^3 + 6^2 + 6
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9

Thus,
399 = 7^3 + 7^2 + 7