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:

Jeff Killed Mike

1. Jack is not the murderer, because he is the brother of the murderer.
2. Dan can't be the murderer since he ran a marathon, and the murderer recently had his leg amputated, and wouldn't be running a marathon of any magnitude that quickly.
3. Ben is not the murderer if he just met Jack, since Jack and the murderer grew up together.
4. This leaves Jeff and Mike.

Since Jeff is still alive (he wants to install a new computer next week, present tense) he must be the murderer. Mike also didn't grow up with Jack. It has been determined that Jack, Dan and Jeff are all alive. Ben must also be alive since Jeff plans to install Ben's computer next week. This means that Jeff killed Mike.

Solution:

The women is a of short stature. She can't reach the upper elevator buttons, but can push is with his umbrella.

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Solution:

he was genius.

Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute.

Solution:

The person who is dead is B.

The presence of numerous flies around foot B strongly indicates that this individual has passed away.

Solution:

The girl in the red shirt.
As she is eating a sandwich that looks like it's years old, and that might kill her.

Solution:

Felice & Nicolas.

The number corresponding to the atomic number of the elements.
26-3-58 (FE-li-ce) =>Felice
28-27-57-16(Ni-co-la-s) => Nicolas.

Also explained in the video.

Solution:

The poison was not in pills but in water.

Solution:

When blind man "Grandpa" opened his bandages, the train must be passing through the dark tunnel. The man thought he was still blind and hence commit suicide.