What is the next number in this matchsticks series riddle?

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

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

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

With pointed fangs I sit and wait; with piercing force I crunch out fate; grabbing victims, proclaiming might; physically joining with a single bite. What am I?

Can you count the number of children in the picture below

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?