Solution:

One of 57620 or 57628 must be the secret code.

Explanation:
Hint-1: 79314
Only 7 is there and in wrong

Hint-2: 95643
6 is in the right position while 5 is not

Hint-3: 57319
5 and 7 are in the right position

Sum Hint: A + B + C + D + E = D*10 + E
CaseA - 57620
5 + 7 + 6 + 2 + 0 = 2 * 10 + 0
20 = 20

CaseB - 57628
5 + 7 + 6 + 2 + 8 = 2 * 10 + 8
28 = 28

Solution:

7 Trips

Explanation:
Send 2+5+9 = 16
Bring back 9
Send 3+4+9 = 16
Bring back 9
Send 1+7+8 = 16
Bring back 1
Send 1+6+9 = 16

Solution:

A

Explanation:
On Picture B and C, the boy is holding the man while in picture A the man is holding the boy.

Solution:

The cowboy can fit the horses as shown below.

[T] [E] [N] [H] [O] [R] [S] [E] [S]

Solution:

Pour 3 lumps on cup-1 and cup-3 and 4lumps on cup4 and place them as shown in the picture.

Explanation:
Now,
Cup-1 got three sugar lumps
Cup-3 got three sugar lumps
Cup-2 got three seven lumps (3 of cup-1 and 4 of its own)

Solution:

Yes

Explanation
-> White starts the game with the knight
-> black move the pawn in the position of the picture.
-> White brings the knight to the original position.

Solution:

As the balloon lost altitude, all of the thieves took off their clothes in order to decrease the overall weight. but when balloon continues to lose the attitude they decide one of them need to jump to the desert to decrease the weight.
The man who must jump is decided by the famous death game where one who picks the shortest toothpick must die.
Frank Catton pick the half toothpick and was already naked and hence the hence explain his state in the desert.

Solution:

It can be done as shown in the picture below. Key to solving such problems is to fill the prime number first.

Solution:

3

Explanation:
Possible matches
Chelsea vs Tottenham
Chelsea vs ManCity
Chelsea vs Arsenal
Chelsea vs Liverpool
Tottenham vs ManCity
Tottenham vs Arsenal
Tottenham vs Liverpool
ManCity vs Arsenal
ManCity vs Liverpool
Arsenal vs Liverpool

Therefore there is a total of 10 matches. After every match, 2 points were distributed between two teams as:
Case1: One of team wins:
Winning team will get 2 points.

Case2: Match ends up in a draw
Both teams will share a point.

Therefore 10*2 = 20 points should be the sum of all team points.

6 + 5 + 4 + 2 + ? =20
? = 3

Solution:

Turn the equation to 180 degrees (upside down)

16 = 8 + 8.