What is both possible and impossible at the same time?

I know a nine-letter word having only one vowel.
Do you ?

John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. 'Does John lie?' The person replied with a yes.

Whom did I talk with, John or Jacob?

What is the probability of choosing the correct answer at random from the options below?

a) 1/4
b) 1/2
c) 1
d) 1/4

I am a white box having no key or lid.
Yet there is a golden treasure inside it.

What Am I?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

He does not have any heart but still, He manages to live.
If you kill him, you will eventually die but yet you kill him.
He cannot run, who is He?

In the following series, a set of numbers is progressing with a particular pattern. Can you deduce that pattern and find the missing set?

(2 + 6), (21 + 6), (58 + 6), (119 + 6), ___

I am a type of food that is often found in the fridge and can be white in colour. What I am?
Hint 1: I am a dairy product.
Hint 2: You can spread me on the bread.

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?