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

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

John: "Hi Teacher, What is your favourite movie ?".
Chemistry Teacher: "Indium Cerium Platinum Iodine Oxygen Nitrogen".
Ten seconds later... John replied I got it.

Do you?

What can jump higher than a building?

What question can you never answer yes to?

What's a single-digit number with no value?

What occurs twice in a week, once in a year but never in a day?