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:

It can be done as shown below.

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.

Solution:

6

Explanation:
Key1: 3 attempts for 3 gates.
Key2: 2 attempts for remaining 2 gates.
Key3: 1 attempts for the last gate.

Solution:

11

Explanation:
Tzu‑ying won 3 games
V.Sindhu must win 3(to balance 3 games she lost) + 5 games(required for min 50$) = 8 games
Total Games = 3 + 8 = 11 games.

Solution:

The poison was not in pills but in water.

Solution:

When blind man "Grandpa" opened his bandages, the train must be passing through the dark tunnel. The man thought he was still blind and hence commit suicide.