What does the below rebus riddle means?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

John named his first son Alpha, second Beta, third Charlie and fourth Delta. What is the fifth son's name?

You are given 2 eggs.
You have access to a 100-storey building.
Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor, Both eggs are identical.
You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

Doctor Alex and a bus driver John are both in love with the same woman named Olivia. The bus driver need to go for a long trip of 10 days, Before he left he gave Olivia 10 apples.

Can you tell a 3D object that has just two surfaces?

Find the number of squares in the below picture

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?