Can you find a five letter word that is left with only two letters if one is removed?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

I am a five-letter word and people eat me. If you remove the first letter I become an energy form. If you remove the first two letters, I am needed to live. Scramble the last three letters and I am a drink. What word am I?

They are three errirs in this question. Can you find them?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?