Using Only Five 5's and any mathematical operator make sum as 37

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

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

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.

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

Identify Me

Hint1: I am a god
Hint 2: I am a planet
Hint 3: measurer of heat

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?