Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

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]

In a concert, Christina is performing a dance show with her group.
At 10:00, she and her crew were dancing in an absolutely straight line. At that time Christina was standing in 4th position from both the front and back end of the row.

What was the size of her crew?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

The more of this there is, the less you see. What is it?

You have 1023 apples and 10 bags. You have to distribute these apples in these 10 bags in any way you choose. But when I ask for a certain number of apples you have to give them in terms of bags without transferring the apples from other bags. How do you distribute the apples?

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

I go up and I go down.
I go up towards the beautiful sky and down toward the green ground.
I am present tense.
I am past tense too
Children love me.

Who Am I?

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?