What is more useful when it is broken?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

What do you call a fish without an eye?

To attend world science seminar, A famous chemist from Mexico visit
London. In the lab, the scientist was killed and his six assistants were under suspicion of killing the chemist.
Name of six assistants: Austin, Wayne, Dege, Oscaru, Lingard, and Rojo.
He left a note "76-20-44 79-16-22-7"

A local detective Jack was called to solve the case,

After reading the note, Jack instantly asked the police to arrest the murderers.

Who are the murderers?

What Does this text mean:

important=important

What number comes next in this sequence:
7 8 5 5 3 4 4 _

Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?