When we see 2 but call 10?

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

A man escapes from jail using help from his girlfriend. The investigators suspect four girls of being the man's girlfriend.

Out of those four girls, one is his girlfriend who is lying. Two of the girls are completely innocent and are speaking the truth. One of the girls is the man's sister who is helping the girlfriend lie. Following are the statements from all four of them:

Ariana: "Myrna is his girlfriend."
Jane: "Angelina is lying."
Angelina: "Ariana is lying."
Myrna: "Jane is not his sister."

Can you find out who is the man's sister among them?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

Akbar summoned Birbal out of anger.
He told him that he will have to face death.
He asked him to make a statement and if the statement is true he will be buried alive and if the statement is false, he will be thrown at lions.
After hearing Birbal’s statement, Akbar could do nothing but smile.
He gave him 5 gold bars and let him go.

What did Birbal say?

Give it food and it will live; give it water and it will die.

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?