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

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

Why did the Girl throw the butter out of the window?

John asked Jack, "The time right now is 7 pm. Can you tell me what will be the time 23, 999, 995 hours later ?"

While Bella does not know the answer, do you ?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

Imagine you are in a room with no windows or doors. How will you get out?

Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186

Now deciphering the way it has been coded, can you find out how September will be coded?