People put me on the table and cut me but do not eat me. What am I?

A man has eighty-one cows ( numbered 1,2,3...81 as such). The beauty is that cow no. 1 gives 1ltr of milk, cow no. 2 gives 2ltrs of milk and so on. The man wants to equally distribute the cows among his nine sons so that each one of them gets the same quantity of milk.

Mr. Buttons was all set to go to the village of Buttonland to meet his friend. So, he packed his bags and left for the village at 5 in the morning. Upon travelling on a road for miles, he came across a point where the road diverged into two. He was confused on which road to take. He gazed around and he saw two owls sitting on a branch. He thought he could ask for directions for the village from the two owls. So he went to the tree. There he saw a sign which read, "One owl always lies, and one is always truthful. They both fly away if you ask them more than 1 question."
Mr. Buttons was caught in the dilemma of what to ask? And from which owl to ask, since he only had one question. What should Mr. Buttons ask?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

By what process could you make a 'Tea-Table' into food?

Why is 6 afraid of 7?

Paul's height is six feet, he's an assistant at a butcher's shop and wears size 9 shoes. What does he weigh?

Why did the Girl throw the butter out of the window?

Can you solve below mathematical equation?

2^1234 - 2^1233

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?