Solve below rebus puzzle?

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

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

Why is it very easy to weigh a fish?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

How many runs at maximum can a batsman score in a normal one-day match? Consider the fact that the conditions are ideal and there are no No Balls, no Wide Balls and no Extras in that match.

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

I shave every day, but my beard stays the same. What am I?