Danny

B, D and E are the liars.
First, if A was a liar, then C would be a liar. But then D would say the truth, which contradicts A’s statement about B lying. Therefore, A says the truth. That means C also says the truth. You can use logic to prove that this doesn’t make a contradiction.

The woman has an incredible, debilitating fear of flying. She must travel to see a dying relative which adds to her emotional disposition. Upon entering the plane she is overcome with fear and her husband consoles her. The flight takes a few hours and upon arrival they are allowed to leave the plan.

18 eggs.

1 chicken lays 2 eggs in 3 days, so 3 chickens lay 3×2=6 eggs in 3 days. In 9 days, these 3 chickens lay 3 times as much eggs as in 3 days. Conclusion: three chickens lay 3×6=18 eggs in nine days.

One of the coins is really not a nickel because nickel is the other coin.

Winter gloves

A banana.

Pennsylvania (Pencil-vania).

20, 28 (two series – every second number: 11, 14, 17, 20 and 19, 22, 25, 28)

The letter E.

Mist.

There is just one P in a 'pint'.