How can you tell a raw egg from a hard-boiled egg?

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?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

Andrew sees a very rare bird named "Ruppell's vulture". Soon Andrew was dead. Can you explain the mystery, Mr. Sherlock?

Why is 6 afraid of 7?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?

What makes this number unique: 8,549,176,320?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?