Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

I am quite hot but become too cold if you remove the first two letters. What am I?

John is on an island and there are three crates of fruit that have washed up in front of him. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

Each crate is labelled. One reads 'apples', one reads 'oranges', and one reads 'apples and oranges'. He know that NONE of the crates have been labeled correctly - they are all wrong.

If he can only take out and look at just one of the pieces of fruit from just one of the crates, how can he label all of the crates correctly?

A man lives on the fifteenth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator, or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up five flights of stairs to his apartment. Can you explain why he does this?

What is the next number in this series?

4,12,84,3612....

It walks on 4 when its young, walks on 2 when it's older, and walks on 3 when its very old?

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

Spot 5 differences in two Christmas tree below:

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).