Solution:

Sheldon filled a Mug with water and held it over his head for 10 minutes.

Solution:

East

Explanation:
- Right Turn => North Direction
- About Turn => south Direction
- Left Turn => East Direction

Solution:

The prisoner picks a marble and without showing it to anyone swallows it and then picks the remaining marble and shows to everyone which was black which proved the first marble prisoner pick must be white.
The Mad King has no option but to let the prisoner go.

Solution:

The Letter L

Solution:

The man is dead and not mute.

Solution:

Frank was born in room #1933

Solution:

9

1(Mr. Beckham) + 1(Mrs. Beckham) + 6 (daughters) + 1 (brother).

Solution:

Velma waits until night time and then goes through the second door.

(No sun at night)

Solution:

Just 1

Solution:

6