What brings you down but never up?

What does the below rebus riddle means?

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

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

John went to meet his friend Jacob, but when he was about to reach the main gate, John notices that Jacob had a mighty dog who was fastened to the tree. The chain is long enough that it allows the dog to reach the main gate.

How can the John reach the main gate?

How can you take 2 from 5 and leave 4?

If 24H in a D => 24 hours in a day.
What does "64S on CB" stand for?

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

In the given figure, you can see that four match sticks are used to form a square. Can you form five squares by using six matches?