Can you decipher the below rebus?

PBLUESAISNUERSES

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?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

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

If eleven plus two equals one, what does nine plus five equal?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

You are confined in a room and given two metal rods. Out of these two rods, one is magnet and the other is the iron rod. They look starkly similar. You don't have any other metal object in the room.

How will you decide which one of those is magnet?

You see me once in June, twice in November, and not at all in May. What am I?

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?

If Rajina's daughter is my daughter's mom, who am I to Rajina?