Solution:

There can be various solutions. Here are a few that we came up with: 1 + 2 + 4/6 + 5 + 7/3 + 89 = 100
12 + 6/3 + 75 + 8/4 + 9 = 100
1/6 + 2 + 4/8 + 7/3 + 95 = 100
24 + 57 + 6/3 + 8 + 9/1 = 100
36 + 4/8 + 51 + 7/2 + 9 = 100
3/2 + 5 + 6/8 + 7/4 + 91 = 100

Solution:

Can be found on the pic below.

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

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:

Let us denote the number of boys as 'p' and the number of girls as 'q'.

The first statement says that each boy has equal numbers of brothers and sisters
(p - 1) = q
=> p - q = 1 ------- (a)

The second statement says that every girl has twice as many brothers as that of sisters
2 (q - 1) = p
=> 2q - p = 2 ------- (b)

By solving (a) and (b)
We get q as 3 and p as 4.

Therefore, there are 4 boys and 3 girls in the family.

Solution:

The bridge won't break.

When the car has travelled half of the bridge, that is 15km, the car must have used more than 300 grams of fuel. Therefore, the impact of bird's added weight will be zero literally.

Solution:

She is near the trunk of the tree as shown below.

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:

It will take the man 58 minutes to reach the top.

Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.

Solution:

At first, there were 2 apples on the tree. After the wind blew, one apple fell on the ground. So there where no apples on the tree and there were no apples on the ground.
*apples => more than one apple

Another solution(non tricky one)
The wind blew so hard that the apples fell of the tree and blew along the ground.

Solution:

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules