Can you find out the remainder when 3^300 is divided by 5?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

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

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

How can you write nineteen in a manner that if we take out one, it becomes twenty?

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?

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?

I know a ten-letter word in the English language which can be typed using only the top rows of the computer keyboard.

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?