Solution:

The two statements have given it out. If you read carefully, you will easily be able to deduce the answer.

We know that everybody is wearing a different color than their names. Now let us begin with the man who noticed the first i.e. Mr. Grey. He is wearing either Pink or Orange. But in the second statement, we already know that the person who is wearing Pink is somebody else. Thus Mr. Grey must be wearing a Orange shirt.

Mr. Pink cannot wear Pink shirt and Orange shirt has already been taken, thus he must be wearing a Grey shirt.

This leaves only one choice for Mr. Orange and he must be wearing a Pink shirt.

Solution:

The killer is Alice.
The number in front of the month's name in the note actually points towards the position of a particular letter in every month.
Second of January = A
Third of July = L
Fourth of April = I
Second of October = C
Fourth of December = E.

Thus, the name is Alice.

Solution:

Newspaper delivery man was the murderer because of absence of Wednesday and Thursday missing newspaper.
This indicates he already know that there is no one to read it.

Solution:

Wayne Rooney stole socks
Danny welbeck stole shoes
Robin Persie stole football

Solution:

She simply asked everyone to raise hands on hearing the question. The only condition was that the ones who knew the correct answer will raise right hand and other will raise left hand facilitating her in acknowledging the ones to pick for answering.

Solution:

Megan (9:00AM) - Keira (11:00AM) - Penelope (8:00PM) - Charlize (10:00PM)

From the given data, it is clear that at least one female visited me in the morning and at least one female visited me in the evening. Also, from (4), Penelope did not visit me first. It means that Penelope visited me at 8:00 PM. From (3), Megan must have visited me at 9:00 AM. Also, either Charlize or Keira or both visited me in the morning. But from (2), only Keira must have visited me in the morning at 11:00 AM and hence, Charlize visited me at 10:00 PM.

Solution:

From top to bottom, the flavors are :

nutty-chocolate
peppermint
orange
Jamaica
walnut

Solution:

As we have been informed that the prices are a full dollar increment, this eases out the situation.

If we look at the price of pineapple and capsicum, we can easily make out that both of them are priced $1.
This is because the price has to be at least $1 and since both of them costs $2 together, they must cost $1 separately.

Solving the rest of the question is child’s play. You have to use simple mathematics.

For an instance:
Jalapeno + Pineapple = $5
Now, we know that pineapple costs $1. Thus,
Jalapeno + $1 = $5
Jalapeno = $4

You can find out the price for each one of the toppings in a similar fashion.
Capsicum $1
Pineapple $1
Mushrooms $3
Corn $2
Jalapeno $4
Red Pepper $2
Black Pepper $3
Olives $4

Solution:

I have written 'your exact weight' on the paper.

Solution:

You can put one precious stone in any one of the bag and all the rest in the other bag. If you do it, you will get just a shade under ¾ probability of picking up a precious stone.