What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

A man says, "Brothers and sisters, have I none, but that man's father is my father's son." Who is that man?

If your uncle’s sister is not your aunt, what relation is she to you?

John is a strange liar.

He lies on six days of the week, but on the seventh day, he always tells the truth.

He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it"s Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

On which day does John tell the truth?

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

Always in you, Sometimes on you;

If I surround you, I can kill you.

What am I?

Different lights make me strange by changing me into different sizes. What am I?

What has many keys but can’t open a single lock?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

There is a box. The area of its top is 240 square units, the area of the front is 300 square units and the area of the end is 180 square units.

Can you calculate the dimensions of this box with the given data?