Solution:

13 8

prime number and then number of letter in prime number

examples
2 (two - 3 letters) => 2,3
3 (three - 5 letters) =>3,5

Solution:

9

Explanation:
2 < 3 < 5
To find out the required number of candies, take one in place of the least number (i.e. take one mango candy) and then add all the greater numbers (i.e. three strawberry and five pineapple candies) to it.

Required number of balls = 1 + 3 + 5 = 9.

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

The Password.

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

Solution:

Kid1, he was left with one rock.

Solution:

Solution is shown in image below

Solution:

This statement is true but only in a specific case i.e. if both of the siblings continue to live till the day the younger is as old as the elder one was during the time of their birth.

Solution:

Put one black rock in one sack and put all the rest in the other one. In such manner you will get about 3/4 probability of surviving.

Solution:

The matchsticks that are marked with red are to be removed and the final figure will have just two squares. You can remove either pair from the possible four ways.

Solution:

On the back, since bullet train is accelerating, therefore,the person at the back will spend less time than one in front.

Solution:

A Spider