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

Name the three-letter word that can complete the below words:

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

What does an Island and the letter T have in common?

Detective John was investigating a murder in China.
It was a difficult case, and John was completely stumped until he noticed a message sent to him by the killer cunningly hidden in a newspaper advertisement selling Car Licence Plates.
Detective John thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.

Q1) How did John know the advert was a clue for him?

Q2) Solve the code and tell me who John arrested.

This is the newspaper advert (Car licence plates for sale) that Detective John saw.

Plates For Sale;

[W 05 NWO]
[H 13 HSR]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Solve below popular number sequence
314 159 265 358 979 323 846 ?

What is both possible and impossible at the same time?

What month of the year has 28 days?

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?