Solution:

Add two squares as shown in the picture below.

Solution:

Image
https://gpuzzles.com/new/img/riddles/Presence-Of-Mind-Picture-Riddle.png
can be changed to
https://gpuzzles.com/new/img/riddles/Presence-Of-Mind-Picture-RiddleAns.png
By adding 3 letters "Ans".

Solution:

U472BMT

Explanation:
The code can be decoded to sound as "U four seven two B M T"
U
four (4)
seven (7)
two (2)
B
M
T

Solution:

Mahrez Pick 4 marbles.

Explanation:
How many marbles Vardy picks, Mahrez needs to make sure that only 1 marble is left after his move, So Vardy needs to pick the last marble.

Example:
If Vardy picks 1, Mahrez picks 5
If Vardy picks 2, Mahrez picks 4
....
...
If Vardy picks 5, Mahrez picks 1

Solution:

31

Explanation:
Ramanujan lighting the candles in binary.
11110 =30
11111 =31

Solution:

3

Explanation:
Digits are represented in binary form where a ball is 1 and a ring is 0.
001 = 1
010 = 2
100 = 4
011 = 3

Solution:

Felix

Explanation:
Iron = Fe (chemical symbol)
59 = LIX (Roman numerals)

Solution:

It can be done as shown below in the picture.

Solution:

Adam betrayed Eve.

Explanation:
Eve may not jump because of the survival instinct or can be related to some emotions and can, therefore, be given a benefit of the doubt, whereas Adam having the parachute seem a calculated plan implies that he definitely betrayed Eve.

Solution:

No

Explanation:
Assume that the rope can be stretched forever. Assume the rope is evenly stretched. The moving speed of the end point of the rope (relative to the starting point) is 1000 cm/second.

Each second the ant moves 1cm, at the same time that 1cm rope stretches to be 1000+1000t1000+1000(t−1)= t+1tcm where t is the number of seconds after the ant is on the rope. Therefore, the ant has a moving speed of t+1t cm/second.

Therefore, the moving speed of the ant is far less than the moving speed of the end point of the rope.

Filk will never reach the end of the 1000 cm long rope.