Solution:

97

Explanation:

Difference between number sequence is below:
9,14,19,24,29

Now the difference between above sequence is 5.

So next number is 68 + 29 =>97

Solution:

When you were inside the shed, the murderer replaced the lock with his own one that was identical to your original lock. When you locked the store room, you did not require a key and there was nothing abnormal for you. When you left, the murderer opened the lock with his key, planted the dead body inside and replaced the lock again putting the original lock in the place. He then closed it without any problem.

Solution:

54325

Explanation:

Consider 1 = 5
2 = 25
3 = 325
4 = 4325
Then 5 = 54325

See the pattern. With every digit, the previous numbers are added after that digit

So the next number in the series is 54325

Solution:

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

Solution:

Start singing the Happy Birthday song and the lion will run towards the candle and blow it.

Solution:

Arc + tick + circle.
= Artic Circle

Solution:

Adam and Eve were the only people without navel. As they were not born out of a mother, they never had umbilical cords and thus never had navels.

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

The person is leaving hospital after visiting his wife. His wife is on a life support system. The elevator has stopped due to the power cut. If there was an emergency backup generator functioning well, the elevator would have also be running. It stopped in between means that the life system support has stopped as well.

Solution:

The woman started walking across the bridge when the guard was inside the hut. She walked all the time he was inside (5 minutes) and then turned and moved back towards the kingdom. On approaching the kingdom he was asked for papers and since she did not have any, she was sent back.