What is both possible and impossible at the same time?

I have branches, but no fruit, trunk or leaves. What am I?

Rumel, A detective who was mere days from cracking an international smuggling ring has suddenly gone missing. While inspecting his last-known location, you find a note:

710 57735 34 5508 51 7718

Currently, there are 3 suspects: Bill, John, and Todd. Can you break the detective's code and find the criminal's name?

A prisoner is told: "If you tell a lie, we will hang you and if you tell the truth, we will shoot you." What did the prisoner say to save himself?

Count the squares in the matchstick puzzle below?

Identify Me

Hint1: I am a god
Hint 2: I am a planet
Hint 3: measurer of heat

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

You want to boil a two-minute egg. If you only have a three-minute timer (hourglass), a four-minute timer and a five-minute timer, how can you boil the egg for only two minutes?

Name a key which is hardest to turn.