Solution:

The man is dead and not mute.

Solution:

The Letter L

Solution:

The old man gave the clerk four quarters so it's obvious that he needed two tickets, Otherwise, he would have only given 2 quarters.

Solution:

No glass will ever fill.

Explanation:
Outlet to Glass-1 & 5 is blocked at the initial point, so they won't fill.
Outlet to Glass-2 is blocked at the endpoint, so it won't fill.
Outlet to Glass-3, 4 & 7 is also blocked in the middle, so they won't fill.
Nothing is connected to Glass-6.

Solution:

The Bomb will explode in just 5 minutes and he can use that exit afterward.

Solution:

Coffee.

The person with two a's drink coffee.
The person with two e's drink coke.
By the same logic, Armando drinks coffee.

Solution:

The Waiter

Holding a tray is a static job while serving dishes and drinks is their main work and hence the waiter is most likely the left-handed person.

Solution:

Sunday

Explanation:
Since each day of the week is repeated after 7 days.
So, after 77 days, it will be Tuesday.
Therefore, After 75 days, it will be Sunday.

Solution:

Pizza

Explanation:
Pizza is served to people with 2 E's and rest are served Burgers.

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.