What does below Rebus mean ?

esgg sgeg gegs gsge

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

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

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

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

What has a bottom at the top?

What country can make you shiver?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

Which country gets ill every time?

What English word has three consecutive double letters?